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

Find ddz(2z3+sin⁡z) \frac{d}{d z}\left(2 z^{3}+\sin z\right) \newlineAnswer:

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Full solution

Q. Find ddz(2z3+sin⁡z) \frac{d}{d z}\left(2 z^{3}+\sin z\right) \newlineAnswer:
  1. Apply Power Rule: To find the derivative of the function with respect to zz, we need to apply the power rule to the term 2z32z^{3} and the derivative of the sine function to the term sin⁡(z)\sin(z).
  2. Simplify Result: Applying the power rule to 2z32z^{3}, we get 3×2z23 \times 2z^{2}, which simplifies to 6z26z^{2}.
  3. Derivative of sin⁡(z)\sin(z): The derivative of sin⁡(z)\sin(z) with respect to zz is cos⁡(z)\cos(z).
  4. Combine Derivatives: Combining the derivatives of both terms, we get the derivative of the entire function: ddz(2z3+sin⁡(z))=6z2+cos⁡(z)\frac{d}{dz}(2z^{3}+\sin(z)) = 6z^{2} + \cos(z).

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