Find (d)/(dz)(3z^(3)+4sin z) Answer:

Apply Power Rule: To find the derivative of the function 3z^(3)+4sin(z) with respect to z, we need to apply the power rule for the polynomial term and the derivative rule for the trigonometric function.Apply Trig Derivative Rule: The power rule states that the derivative of z^n with respect to z is n*z^(n-1). Applying this to the term 3z^(3), we get 3*3*z^(3-1) = 9z^(2).Combine Derivatives: The derivative of sin(z) with respect to z is cos(z). Therefore, the derivative of 4sin(z) with respect to z is 4cos(z).Combining the derivatives of both terms, we get the derivative of the entire function: (d)/(dz)(3z^(3)+4sin(z)) = 9z^(2) + 4cos(z).

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find $\frac{d}{d z}\left(3 z^{3}+4 \sin z\right)$ $\newline$ 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^{3}+4 \sin z\right)

\newline

Answer:

Apply Power Rule: To find the derivative of the function $3z^{3}+4\sin(z)$ with respect to $z$ , we need to apply the power rule for the polynomial term and the derivative rule for the trigonometric function.
Apply Trig Derivative Rule: The power rule states that the derivative of $z^n$ with respect to $z$ is $n*z^{(n-1)}$ . Applying this to the term $3z^{3}$ , we get $3*3*z^{(3-1)} = 9z^{2}$ .
Combine Derivatives: The derivative of $\sin(z)$ with respect to $z$ is $\cos(z)$ . Therefore, the derivative of $4\sin(z)$ with respect to $z$ is $4\cos(z)$ .
Combine Derivatives: The derivative of $\sin(z)$ with respect to $z$ is $\cos(z)$ . Therefore, the derivative of $4\sin(z)$ with respect to $z$ is $4\cos(z)$ .Combining the derivatives of both terms, we get the derivative of the entire function: $\frac{d}{dz}(3z^{3}+4\sin(z)) = 9z^{2} + 4\cos(z)$ .