Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find the derivative of the following function.

y=2^(-x^(2))
Answer:
y^(')=

Find the derivative of the following function. $\newline$ $y=2^{-x^{2}}$ $\newline$ Answer: $y^{\prime}=$

View step-by-step help

View step-by-step help

Find derivatives of radical functions

Full solution

Q. Find the derivative of the following function.

\newline

y=2^{-x^{2}}

\newline

Answer:

y^{\prime}=

Identify function components: Identify the function and its components. $\newline$ We have $y = 2^{-x^2}$ , which is an exponential function with a negative quadratic exponent.
Apply chain rule: Apply the chain rule for differentiation. $\newline$ The chain rule states that the derivative of a composite function is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. $\newline$ In this case, the outer function is $2^u$ and the inner function is $u = -x^2$ .
Differentiate outer function: Differentiate the outer function with respect to $u$ . The derivative of $2^u$ with respect to $u$ is $(2^u \cdot \ln(2))$ , where $\ln(2)$ is the natural logarithm of $2$ .
Differentiate inner function: Differentiate the inner function with respect to $x$ . The derivative of $-x^2$ with respect to $x$ is $-2x$ .
Apply chain rule with derivatives: Apply the chain rule using the derivatives from steps $3$ and $4$ . $\newline$ $y' = \frac{d}{dx}[2^{-x^2}] = (2^{-x^2} \cdot \ln(2)) \cdot (-2x)$
Simplify derivative expression: Simplify the expression for the derivative. $\newline$ $y' = -2x \cdot 2^{-x^2} \cdot \ln(2)$ $\newline$ This is the derivative of the function $y$ with respect to $x$ .

More problems from Find derivatives of radical functions

Question

Find the derivative of

f(x)

\newline

f(x) = \cos(x)

\newline

f'(x) =

Posted 1 month ago

Question

Find the derivative of

f(x)

\newline

f(x) = \tan(x)

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = e^x

\newline

f'\left(x\right) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \ln(x)

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

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

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = x e^x

\newline

f'\left(x\right) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

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

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

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

\newline

f'\left(x\right) =

Posted 1 month ago

Question

Find the derivative of

f(x)

\newline

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

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

g(x)

\newline

g(x) = \ln(2x)

\newline

g^{\prime}(x) =

Posted 3 months ago