Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the derivative of $f(x)$ $f(x)=e^{(x+1)}$

View step-by-step help

View step-by-step help

Find derivatives using the quotient rule I

Full solution

Q. Find the derivative of

f(x)

f(x)=e^{(x+1)}

Find Derivative of $e^{(x+1)}$ : We need to find the derivative of the function $f(x) = e^{(x+1)}$ . The derivative of $e^u$ , where $u$ is a function of $x$ , is $e^u$ times the derivative of $u$ with respect to $x$ . In this case, $u = x + 1$ .
Apply Chain Rule: The derivative of $u = x + 1$ with respect to $x$ is $1$ , since the derivative of a constant is $0$ and the derivative of $x$ is $1$ .
Calculate Final Derivative: Applying the chain rule, the derivative of $f(x)$ with respect to $x$ is $e^{(x+1)}$ times the derivative of $(x+1)$ with respect to $x$ , which we found to be $1$ .
Calculate Final Derivative: Applying the chain rule, the derivative of $f(x)$ with respect to $x$ is $e^{(x+1)}$ times the derivative of $(x+1)$ with respect to $x$ , which we found to be $1$ .Therefore, the derivative of $f(x) = e^{(x+1)}$ is simply $e^{(x+1)} \times 1$ , which simplifies to $e^{(x+1)}$ .

More problems from Find derivatives using the quotient rule I

Question

Find the derivative of

f(x)

\newline

f(x) = \cos(x)

\newline

f'(x) =

Posted 7 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan(x)

\newline

f'(x) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^x

\newline

f'\left(x\right) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \ln(x)

\newline

f'(x) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan^{-1}{x}

\newline

f'(x) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \frac{e^x}{x}

\newline

f'(x) =

Posted 9 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^{(x + 1)}

\newline

f'\left(x\right) =

Posted 7 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \sqrt{x+3}

\newline

f'(x) =

Posted 9 months ago

Question

Find the derivative of

g(x)

\newline

g(x) = \ln(2x)

\newline

g^{\prime}(x) =

Posted 10 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant