# Recent questions tagged differentiation

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What is the derivative of $y = x^2$?
What is the derivative of $y = x^2$?What is the derivative of $y = x^2$? ...
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Evaluate $\frac{d}{d x} f(x)$ using the rules for differentiation: $f(x)=-\frac{1}{2} x^{4}-2 x^{3}+\frac{1}{2} \sqrt{x^{5}}$
Evaluate $\frac{d}{d x} f(x)$ using the rules for differentiation: $f(x)=-\frac{1}{2} x^{4}-2 x^{3}+\frac{1}{2} \sqrt{x^{5}}$Evaluate $\frac{d}{d x} f(x)$ using the rules for differentiation: \ f(x)=-\frac{1}{2} x^{4}-2 x^{3}+\frac{1}{2} \sqrt{x^{5}} \ ...
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Find $h^{\prime}(x)$ using the rules for differentiation: $h(x)=2 x^{2}+4 x-1$
Find $h^{\prime}(x)$ using the rules for differentiation: $h(x)=2 x^{2}+4 x-1$Find $h^{\prime}(x)$ using the rules for differentiation: \ h(x)=2 x^{2}+4 x-1 \ ...
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Given: $a=\frac{1}{2} y^{3}+5 y+2$ Determine $\frac{d}{d y} a$ using the rules for differentiation.
Given: $a=\frac{1}{2} y^{3}+5 y+2$ Determine $\frac{d}{d y} a$ using the rules for differentiation.Given: \ a=\frac{1}{2} y^{3}+5 y+2 \ Determine $\frac{d}{d y} a$ using the rules for differentiation. ...
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Find $D_{x} h(x)$ using the rules for differentiation: $h(x)=6 x^{4}-6 x^{3}-5 x^{2}$
Find $D_{x} h(x)$ using the rules for differentiation: $h(x)=6 x^{4}-6 x^{3}-5 x^{2}$Find $D_{x} h(x)$ using the rules for differentiation: \ h(x)=6 x^{4}-6 x^{3}-5 x^{2} \ ...
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Evaluate $g^{\prime}(x)$ using the rules for differentiation: $g(x)=-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} \sqrt[4]{x^{3}}-\frac{4}{3} x^{\frac{1}{2}}$
Evaluate $g^{\prime}(x)$ using the rules for differentiation: $g(x)=-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} \sqrt[4]{x^{3}}-\frac{4}{3} x^{\frac{1}{2}}$Evaluate $g^{\prime}(x)$ using the rules for differentiation: \ g(x)=-\frac{1}{2} x^{\frac{7}{2}}+\frac{3}{4} \sqrt{x^{3}}-\frac{4}{3} x^{\frac{ ...
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Find $\frac{d}{d x} f(x)$ using the rules for differentiation: $f(x)=-3 x^{2}-6 x+6$
Find $\frac{d}{d x} f(x)$ using the rules for differentiation: $f(x)=-3 x^{2}-6 x+6$Find $\frac{d}{d x} f(x)$ using the rules for differentiation: \ f(x)=-3 x^{2}-6 x+6 \ ...
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What are the rules of differentiation?
What are the rules of differentiation?What are the rules of differentiation? ...
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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has
The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has &nbsp; A. no extremum, B. exactly one maximum, C. exactly one minimum, D. exactly ...
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If $\sin x+\cos x=\sqrt{y+\frac{1}{y}}, x \in[0, \pi]$, then:
If $\sin x+\cos x=\sqrt{y+\frac{1}{y}}, x \in[0, \pi]$, then:If $\sin x+\cos x=\sqrt{y+\frac{1}{y}}, x \in0, \pi$, then: ...
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The number of $x \in[0,2 \pi]$ for which $\left|\sqrt{2 \sin ^{4} x+18 \cos ^{2} x}-\sqrt{2 \cos ^{4} x+18 \sin ^{2} x}\right|=1$ is:
The number of $x \in[0,2 \pi]$ for which $\left|\sqrt{2 \sin ^{4} x+18 \cos ^{2} x}-\sqrt{2 \cos ^{4} x+18 \sin ^{2} x}\right|=1$ is:The number of $x \in0,2 \pi$ for which $\left|\sqrt{2 \sin ^{4} x+18 \cos ^{2} x}-\sqrt{2 \cos ^{4} x+18 \sin ^{2} x}\right|=1$ is: ...
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WHat is the formal definition of the derivative of a function $f(x)$?
WHat is the formal definition of the derivative of a function $f(x)$?WHat is the formal definition of the derivative of a function $f(x)$? ...
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Write down the expansion of $(1+x)^{7}$ in ascending powers of $x$.
Write down the expansion of $(1+x)^{7}$ in ascending powers of $x$.(a)(i) Write down the expansion of $(1+x)^{7}$ in ascending powers of $x$. (ii) If the coefficients of the fifth, sixth and seventh terms in the e ...
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Evaluate: $\int_{1}^{3}\left(\frac{x-1}{(x+1)^{2}}\right) \mathrm{d} x$
Evaluate: $\int_{1}^{3}\left(\frac{x-1}{(x+1)^{2}}\right) \mathrm{d} x$Evaluate: $\int_{1}^{3}\left(\frac{x-1}{(x+1)^{2}}\right) \mathrm{d} x$ ...
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Evaluate $\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x$
Evaluate $\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x$Evaluate $\int_{-1}^{0}(x+1)(x-2) \mathrm{d} x$ A. $\frac{7}{6}$ B. $\frac{5}{6}$ C. $\frac{-5}{6}$ D. $\frac{-7}{6}$ ...
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Find the coefficient of $x^{4}$ in the expansion of $(1-2 x)^{6}$
Find the coefficient of $x^{4}$ in the expansion of $(1-2 x)^{6}$Find the coefficient of $x^{4}$ in the expansion of $(1-2 x)^{6}$ A. $-320$ B. $-240$ C. 240 D. 320 ...
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Evaluate $\int \dfrac{1}{16+x^{2}} d x$
Evaluate $\int \dfrac{1}{16+x^{2}} d x$Evaluate $\int \dfrac{1}{16+x^{2}} d x$ ...
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Evaluate $\int \cos ^{3} x d x$
Evaluate $\int \cos ^{3} x d x$Evaluate $\int \cos ^{3} x d x$ ...
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Use differentiation to find $\mathrm{f}^{\prime}(x)$.
Use differentiation to find $\mathrm{f}^{\prime}(x)$.\ f(x)=x^{3}-3 x^{2}+5 x-4 \ (a) Use differentiation to find $\mathrm{f}^{\prime}(x)$. The equation $\mathrm{f}(x)=0$ has a root $\alpha$ in ...
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Evaluate $\int_{0}^{1} \dfrac{\ln x}{\sqrt{1+x^{4}}}$
Evaluate $\int_{0}^{1} \dfrac{\ln x}{\sqrt{1+x^{4}}}$Evaluate $\int_{0}^{1} \dfrac{\ln x}{\sqrt{1+x^{4}}}$ ...
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Determine $f^{\prime}(x)$ if $f(x)=-4 x^{2}$.
Determine $f^{\prime}(x)$ if $f(x)=-4 x^{2}$.Determine $f^{\prime}(x)$ if $f(x)=-4 x^{2}$. ...
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Determine $f^{\prime}(x)$ if $f(x)=7 x^{2}$.
Determine $f^{\prime}(x)$ if $f(x)=7 x^{2}$.Determine $f^{\prime}(x)$ if $f(x)=7 x^{2}$. ...
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Determine $f^{\prime}(x)$ if $f(x)=-2 x-2$.
Determine $f^{\prime}(x)$ if $f(x)=-2 x-2$.Determine $f^{\prime}(x)$ if $f(x)=-2 x-2$. ...
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Determine $f^{\prime}(x)$ if $f(x)=4 x+7$.
Determine $f^{\prime}(x)$ if $f(x)=4 x+7$.Determine $f^{\prime}(x)$ if $f(x)=4 x+7$. ...
Determine $f^{\prime}(x)$ if $f(x)=-7 x+7$.
Determine $f^{\prime}(x)$ if $f(x)=-7 x+7$.Determine $f^{\prime}(x)$ if $f(x)=-7 x+7$. ...