menu

arrow_back Prove that $\frac{d}{d x}(c f(x))=c f^{\prime}(x)$ using the definition of the derivative.

by Platinum
(119,140 points)
in Mathematics
138 views
Prove that $\dfrac{d}{d x}(c f(x))=c f^{\prime}(x)$ using the definition of the derivative.

Related questions


Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
The derivative \(f^{\prime}(x)\) of \(f(x)\) is defined by
1 answer 201 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Use the definition of derivative to find $f^{\prime}(2)$ for $f(x)=x+\frac{1}{x}$
1 answer 156 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the derivative of $f(x)=\frac{1}{x}$
1 answer 150 views
Find the derivative of $f(x)=\frac{1}{x}$Find the derivative of $f(x)=\frac{1}{x}$ ...
by Pieter Gold Status
(31,957 points)
asked in Mathematics Jun 11, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the derivative of $f(x)=2 x^{2}$
1 answer 105 views
Find the derivative of $f(x)=2 x^{2}$Find the derivative of $f(x)=2 x^{2}$ ...
by Pieter Gold Status
(31,957 points)
asked in Mathematics Jun 11, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
State the definition of the derivative of a function \(g\) at a number \(x\).
0 answers 122 views
close
Based on the table of values for the differentiable, invertible function $f$ and its derivative, evaluate $\left(f^{-1}\right)^{\prime}(2)$.

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Based on the table of values for the differentiable, invertible function $f$ and its derivative, evaluate $\left(f^{-1}\right)^{\prime}(2)$.

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Find the derivative of $y=x^{-3}$. Using the formula, $y^{\prime}=-3 x^{-3-1}=$ $-3 x^{-4} .$ 
1 answer 109 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What does it mean to say that $f(x)$ has a derivative $f^{\prime}(a)$ at $x=a$, and what is the value of $f^{\prime}(a) ?$
0 answers 149 views
What does it mean to say that $f(x)$ has a derivative $f^{\prime}(a)$ at $x=a$, and what is the value of $f^{\prime}(a) ?$Assume that $f(x)$ is a real-valued function defined for all real numbers $x$ on an open interval whose center is a certain real number $a$. What does ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics May 10, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
WHat is the formal definition of the derivative of a function \(f(x)\)?
1 answer 169 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is linearity of a derivative?
1 answer 86 views
What is linearity of a derivative?What is linearity of a derivative? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics Aug 14, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Prove that \(f(x)=\frac{1}{(x+1)^{2}}-2 x+\sin x\) has exactly one positive root.
0 answers 62 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
What is the definition of a "derivative" in calculus?
1 answer 145 views
What is the definition of a "derivative" in calculus?What is the definition of a "derivative" in calculus? ...
by MathsGee Platinum
(119,140 points)
asked in Mathematics May 10, 2021
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
Show that if $f$ is differentiable on $(-\infty, \infty)$ and $f^{\prime}(t) \neq 1$ for all $t$. Prove that $f$ has at most one fixed point.
1 answer 142 views
close

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
The derivative of a function $f$ is given by $f^{\prime}(x)=e^{\sin x}-\cos x-1$ for $0<x<9$. On what intervals is $f$ decreasing?

Notice: Undefined index: avatar in /home/customer/www/mathsgee.com/public_html/qa-theme/AVEN/qa-theme.php on line 993
The function $f$ is differentiable on the interval $(0,4)$. If $f(1)=1$ and $f(3)=7$, then there is at least one $c$ in $(1,3)$ such that $f^{\prime}(c)=$

Q&A | Subjects | Request Private Tutor | eBook


Join the MathsGee Support Club where you get study and financial support for success from our community. LEARN - CONNECT - EARN


On the MathsGee Support Club, you can:


1. Ask questions


2. Answer questions


3. Vote on Questions and Answers


4. Tip your favourite community member(s)


5. Create Live Video Tutorials (Paid/Free)


6. Join Live Video Tutorials (Paid/Free)


7. Earn points for participating



Posting on the MathsGee Support Club


1. Remember the human


2. Behave like you would in real life


3. Look for the original source of content


4. Search for duplicates before posting


5. Read the community's rules




Q&A RULES


1. Answers to questions will be posted immediately after moderation


2. Questions will be queued for posting immediately after moderation


3. Depending on how many posts we receive, you could be waiting up to 24 hours for your post to appear. But, please be patient as posts will appear after they pass our moderation.


Q&A | Subjects | Request Private Tutor | eBook


MathsGee Tools

Math Worksheet Generator

Math Algebra Solver

Trigonometry Simulations

Vectors Simulations

Matrix Arithmetic Simulations

Matrix Transformations Simulations

Quadratic Equations Simulations

Probability & Statistics Simulations

PHET Simulations

Visual Statistics

Q&A | Subjects |Request Private Tutor | eBook