Find (d)/(dz)(3z^(5)-4sin z) Answer:

Apply Power Rule: To find the derivative of the function 3z^(5)-4sin(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 -4sin(z).Derivative of 3z^(5): The power rule states that the derivative of z^n with respect to z is n*z^(n-1). Applying this to 3z^(5), we get the derivative as 5*3z^(5-1) which simplifies to 15z^(4).Derivative of -4sin(z): The derivative of -4sin(z) with respect to z is -4cos(z), because the derivative of sin(z) is cos(z), and we multiply by the constant -4.Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function 3z^(5)-4sin(z) with respect to z as 15z^(4) - 4cos(z).

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Find $\frac{d}{d z}\left(3 z^{5}-4 \sin z\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d z}\left(3 z^{5}-4 \sin z\right)

\newline

Answer:

Apply Power Rule: To find the derivative of the function $3z^{5}-4\sin(z)$ 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 $-4\sin(z)$ .
Derivative of $3z^{5}$ : The power rule states that the derivative of $z^n$ with respect to $z$ is $n*z^{(n-1)}$ . Applying this to $3z^{5}$ , we get the derivative as $5*3z^{(5-1)}$ which simplifies to $15z^{4}$ .
Derivative of $-4\sin(z)$ : The derivative of $-4\sin(z)$ with respect to $z$ is $-4\cos(z)$ , because the derivative of $\sin(z)$ is $\cos(z)$ , and we multiply by the constant $-4$ .
Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function $3z^{5}-4\sin(z)$ with respect to $z$ as $15z^{4} - 4\cos(z)$ .