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)=x^(4)
Write your answer as a constant times a power of
x.

f^(')(x)=
Submit

Find the derivative of $f(x)$ . $\newline$ $f(x)=x^{4}$ $\newline$ Write your answer as a constant times a power of $\mathrm{x}$ . $\newline$ $f^{\prime}(x)=$ $\newline$ Submit

View step-by-step help

View step-by-step help

Full solution

Q. Find the derivative of

f(x)

.

\newline

f(x)=x^{4}

\newline

Write your answer as a constant times a power of

\mathrm{x}

.

\newline

f^{\prime}(x)=

\newline

Submit

Identify Power of $x$ : Rewrite the function in its current form to identify the power of $x$ . The function is already given as $f(x) = x^4$ , which is a power function where the base is $x$ and the exponent is $4$ .
Apply Power Rule: Apply the power rule for differentiation, which states that the derivative of $x^n$ is $n*x^{(n-1)}$ . Here, $n$ is $4$ , so we multiply $4$ by $x$ raised to the power of $4-1$ .
Perform Calculation: Perform the calculation for the exponent. Subtracting $1$ from $4$ gives us $3$ , so the new exponent for $x$ is $3$ .
Write Down Derivative: Write down the derivative. The derivative of $f(x) = x^4$ is $f′(x) = 4x^3$ .

More problems from Power rule II

Question

Find the derivative of

f(x)

\newline

f(x) = x^4

\newline

Write your answer as a constant times a power of

x

\newline

f'(x) =

Posted 2 months ago

Question

Find the derivative of

f(x)

\newline

f(x) = \frac{1}{x^3}

\newline

Write your answer as a constant times a power of

x

\newline

f'(x) =

Posted 2 months ago

Question

Using implicit differentiation, find

\frac{d y}{d x}

\newline

\sqrt{x y}=-6+x y

Posted 2 months ago

Question

Consider the probability density curve plotted below:

\newline

P(X \leq 21): 1 \mid

\newline

P(X>14)

: Epter anineeger or decimal number (more.]

Posted 10 days ago

Question

\newline

\begin{array}{l} f(x)=\frac{1}{6 x}, x \neq 0 \\ g(x)=\frac{1}{6 x}, x \neq 0 . \\ f(g(x))=\square \\ g(f(x))=\square \end{array}

\newline

f

g

are inverses of each other

\newline

f

g

are not inverses of each other

\newline

\newline

Posted 4 days ago

Question

Suppose that the functions

f

g

are defined as follows.

\newline

f(x)=\frac{x}{x-9} \quad g(x)=\frac{8}{x+5}

\newline

\frac{f}{g}

. Then, give its domain using an interval or union of intervals. Simplify your answers.

\newline

\left(\frac{f}{g}\right)(x)=\prod

\newline

\frac{f}{g}

Posted 3 days ago

Question

1.536

96

Posted 24 hours ago

Question

56.8 \times 7.1

Posted 24 hours ago

Question

What is the equation for

g(x)

Posted 24 hours ago

Question

Kirti has developed formulas to help her determine the size of her rectangular flower garden each spring. If she wants to plant

n

varieties of flowers, she determines the length,

L

, and the width,

W

, of her garden, in feet, according to the following formulas:

\newline

\begin{array}{l} L(n)=n+2 \\ W(n)=0.5 n+1 \end{array}

\newline

A

be the area of Kirti's flower garden if she plants

n

types of flowers.

\newline

Write a formula for

A(n)

L(n)

W(n)

\newline

A(n)=\square

\newline

Write a formula for

A(n)

n

Posted 24 hours ago