Find (d)/(dz)(3z^(5)+cos z) Answer:

Apply Power Rule: To find the derivative of the function 3z^(5)+cos(z) with respect to z, we need to apply the power rule to the term 3z^(5) and the derivative of the cosine function to the term cos(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) = 15z^(4).Derivative of cos(z): The derivative of cos(z) with respect to z is -sin(z). Therefore, the derivative of cos(z) is -sin(z).Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function as 15z^(4) - sin(z).

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Find $\frac{d}{d z}\left(3 z^{5}+\cos z\right)$ $\newline$ Answer:

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Q. Find

\frac{d}{d z}\left(3 z^{5}+\cos z\right)

\newline

Answer:

Apply Power Rule: To find the derivative of the function $3z^{5}+\cos(z)$ with respect to $z$ , we need to apply the power rule to the term $3z^{5}$ and the derivative of the cosine function to the term $\cos(z)$ .
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 $5*3z^{(5-1)} = 15z^{4}$ .
Derivative of $\cos(z)$ : The derivative of $\cos(z)$ with respect to $z$ is $-\sin(z)$ . Therefore, the derivative of $\cos(z)$ is $-\sin(z)$ .
Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function as $15z^{4} - \sin(z)$ .