Find (d)/(dz)(3z^(5)-2sin z) Answer:

Apply Power Rule: To find the derivative of the function 3z^(5)-2sin(z) with respect to z, we will apply the power rule to the term 3z^(5) and the derivative of the sine function to the term -2sin(z).Derivative of 3z^(5): Applying the power rule to 3z^(5), we get the derivative as 5 * 3z^(5-1) = 15z^(4).Derivative of -2sin(z): The derivative of -2sin(z) with respect to z is -2cos(z), because the derivative of sin(z) is cos(z) and we need to multiply by the coefficient -2.Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function as 15z^(4) - 2cos(z).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find $\frac{d}{d z}\left(3 z^{5}-2 \sin z\right)$ $\newline$ Answer:

View step-by-step help

Home

Math Problems

Algebra 2

Find trigonometric functions using a calculator

Full solution

Q. Find

\frac{d}{d z}\left(3 z^{5}-2 \sin z\right)

\newline

Answer:

Apply Power Rule: To find the derivative of the function $3z^{5}-2\sin(z)$ with respect to $z$ , we will apply the power rule to the term $3z^{5}$ and the derivative of the sine function to the term $-2\sin(z)$ .
Derivative of $3z^{5}$ : Applying the power rule to $3z^{5}$ , we get the derivative as $5 \times 3z^{5-1} = 15z^{4}$ .
Derivative of $-2\sin(z)$ : The derivative of $-2\sin(z)$ with respect to $z$ is $-2\cos(z)$ , because the derivative of $\sin(z)$ is $\cos(z)$ and we need to multiply by the coefficient $-2$ .
Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function as $15z^{4} - 2\cos(z)$ .