Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find
f^(')(x) where
f(x)=2x cos(x).

Find $f^{\prime}(x)$ where $f(x)=2 x \cos (x)$ .

View step-by-step help

View step-by-step help

Find derivatives of radical functions

Full solution

Q. Find

f^{\prime}(x)

where

f(x)=2 x \cos (x)

.

Identify Components: Identify the components of the function that will require the use of the product rule for differentiation. $\newline$ The function $f(x) = 2x \cos(x)$ is a product of two functions, $g(x) = 2x$ and $h(x) = \cos(x)$ .
Recall Product Rule: Recall the product rule for differentiation, which states that if $f(x) = g(x) \cdot h(x)$ , then $f'(x) = g'(x) \cdot h(x) + g(x) \cdot h'(x)$ . We will apply this rule to find the derivative of $f(x) = 2x \cos(x)$ .
Differentiate $g(x)$ : Differentiate $g(x) = 2x$ with respect to $x$ . The derivative of $g(x)$ with respect to $x$ is $g'(x) = \frac{d}{dx}(2x) = 2$ .
Differentiate $h(x)$ : Differentiate $h(x) = \cos(x)$ with respect to $x$ . The derivative of $h(x)$ with respect to $x$ is $h'(x) = \frac{d}{dx}(\cos(x)) = -\sin(x)$ .
Apply Product Rule: Apply the product rule using the derivatives found in the previous steps. $\newline$ Using $g'(x) = 2$ and $h'(x) = -\sin(x)$ , we get $f'(x) = g'(x) \cdot h(x) + g(x) \cdot h'(x) = 2 \cdot \cos(x) + 2x \cdot (-\sin(x))$ .
Simplify Derivative: Simplify the expression for the derivative. $\newline$ $f'(x) = 2 \cdot \cos(x) - 2x \cdot \sin(x)$ . $\newline$ This is the derivative of the function $f(x) = 2x \cos(x)$ .

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