Find (d)/(dy)(y^(4)-3sin y) Answer:

Apply Power Rule: Differentiate the function y^(4)-3sin(y) with respect to y. We will apply the power rule to y^(4) and the derivative of the sine function to -3sin(y). (d)/(dy)(y^(4)-3sin(y)) = (d)/(dy)(y^(4)) - (d)/(dy)(3sin(y))Power Rule for y^4: Apply the power rule to y^(4). The power rule states that (d)/(dy)(y^(n)) = ny^(n-1). (d)/(dy)(y^(4)) = 4y^(4-1) = 4y^3Differentiate -3sin(y): Differentiate -3sin(y) with respect to y. The derivative of sin(y) with respect to y is cos(y), and we need to multiply this by the constant -3. (d)/(dy)(-3sin(y)) = -3cos(y)Combine Results: Combine the results from Step 2 and Step 3. (d)/(dy)(y^(4)-3sin(y)) = 4y^3 - 3cos(y)

Home

Math Problems

Calculus

Find derivatives of using multiple formulae

Full solution

Q. Find

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

\newline

Answer:

Apply Power Rule: Differentiate the function $y^{4}-3\sin(y)$ with respect to $y$ . We will apply the power rule to $y^{4}$ and the derivative of the sine function to $-3\sin(y)$ . $\frac{d}{dy}(y^{4}-3\sin(y)) = \frac{d}{dy}(y^{4}) - \frac{d}{dy}(3\sin(y))$
Power Rule for $y^4$ : Apply the power rule to $y^{4}$ . $\newline$ The power rule states that $\frac{d}{dy}(y^{n}) = ny^{n-1}$ . $\newline$ $\frac{d}{dy}(y^{4}) = 4y^{4-1} = 4y^3$
Differentiate $-3\sin(y)$ : Differentiate $-3\sin(y)$ with respect to $y$ . The derivative of $\sin(y)$ with respect to $y$ is $\cos(y)$ , and we need to multiply this by the constant $-3$ . $\frac{d}{dy}(-3\sin(y)) = -3\cos(y)$
Combine Results: Combine the results from Step $2$ and Step $3$ . $\newline$ $(d)/(dy)(y^{4}-3\sin(y)) = 4y^{3} - 3\cos(y)$