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^(-5x^(4))
Answer:
y^(')=

Find the derivative of the following function. $\newline$ $y=2^{-5 x^{4}}$ $\newline$ 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^{-5 x^{4}}

\newline

Answer:

y^{\prime}=

Identify components: Identify the components of the function $y = 2^{-5x^{4}}$ . The base of the exponent is a constant ( $2$ ), and the exponent is a function of $x$ ( $-5x^{4}$ ).
Apply chain rule: Apply the chain rule for derivatives. 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.
Derivative of outer function: The outer function is $2^u$ , where $u$ is the inner function $-5x^{4}$ . The derivative of $2^u$ with respect to $u$ is $2^u \cdot \ln(2)$ , because the derivative of $a^x$ with respect to $x$ is $a^x \cdot \ln(a)$ .
Derivative of inner function: The inner function $u(x)$ is $-5x^{4}$ . The derivative of $-5x^{4}$ with respect to $x$ is $-20x^{3}$ , because the derivative of $x^n$ with respect to $x$ is $n\cdot x^{n-1}$ .
Combine derivatives using chain rule: Combine the derivatives of the outer and inner functions using the chain rule. $\newline$ $y' = \frac{d}{dx}[2^{-5x^{4}}] = (2^{-5x^{4}} \cdot \ln(2)) \cdot (-20x^{3})$
Simplify the expression: Simplify the expression for the derivative. $y' = -20x^{3} \cdot 2^{-5x^{4}} \cdot \ln(2)$

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