Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

$\frac{d}{dx}(-2x^{4}-4x^{-2}-4)$

View step-by-step help

View step-by-step help

Multiplication with rational exponents

Full solution

Q.

\frac{d}{dx}(-2x^{4}-4x^{-2}-4)

Identify function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = -2x^{4} - 4x^{-2} - 4$ , and we need to find its derivative with respect to $x$ .
Apply power rule: Apply the power rule for differentiation. $\newline$ The power rule states that the derivative of $x^n$ with respect to $x$ is $n\cdot x^{(n-1)}$ . We will apply this rule to each term in the function separately.
Differentiate first term: Differentiate the first term $-2x^{4}$ . $\newline$ Using the power rule, the derivative of $-2x^{4}$ with respect to $x$ is $-2 \times 4 \times x^{4-1} = -8x^{3}$ .
Differentiate second term: Differentiate the second term $-4x^{-2}$ . Using the power rule, the derivative of $-4x^{-2}$ with respect to $x$ is $-4 \times (-2) \times x^{-2-1} = 8x^{-3}$ .
Differentiate third term: Differentiate the third term $-4$ . The derivative of a constant is $0$ , so the derivative of $-4$ with respect to $x$ is $0$ .
Combine derivatives: Combine the derivatives of all terms. $\newline$ The derivative of the function $f(x)$ with respect to $x$ is the sum of the derivatives of its terms, which gives us $-8x^{3} + 8x^{-3} + 0$ .
Simplify derivative: Simplify the derivative if necessary. $\newline$ In this case, the derivative is already simplified, so we can write the final answer.

More problems from Multiplication with rational exponents

Question

\newline

81^{\frac{1}{2}}

\newline

Posted 9 months ago

Question

\newline

(-32)^{1/5}

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{4}{3}}}{w^{\frac{7}{3}}}

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

(2r^{\frac{1}{3}})^8

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 5 months ago

Question

Simplify. Assume all variables are positive.

\newline

v^{\frac{7}{4}} \cdot v^{\frac{9}{4}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 5 months ago

Question

\newline

1^{\frac{1}{4}} \cdot 1^{\frac{1}{4}}

\newline

Posted 5 months ago

Question

\newline

32^{(-1/5)}

Posted 7 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{w^{\frac{3}{2}}}{w^{\frac{5}{2}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 9 months ago

Question

Simplify. Assume all variables are positive.

\newline

(27x)^{\frac{2}{3}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

Posted 8 months ago

Question

Simplify. Assume all variables are positive.

\newline

\frac{x^{\frac{1}{4}}}{x^{\frac{11}{4}}}

\newline

\newline

Write your answer in the form

A

\frac{A}{B}

A

B

are constants or variable expressions that have no variables in common. All exponents in your answer should be positive.

\newline

\newline

Posted 7 months ago

Related topics

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