Differentiate the function. $B(y)=c y^{-4}$
A) $B^{\prime}(y)=\frac{5 c}{y^{4}}$
B) $B^{\prime}(y)=-\frac{5 c}{y^{4}}$
C) $B^{\prime}(y)=-\frac{4 c^{5}}{y}$
D) $B^{\prime}(y)=-\frac{4 c}{y^{5}}$
E) $B^{\prime}(y)=-\frac{c}{4 y^{5}}$

Question

Quizplus · Accepted Answer

We differentiate the function using the power rule of differentiation:
$$B'(y)=\frac{d}{dy}\left(c y^{-4}\right)=-4c y^{-5}=-\frac{4c}{y^5}$$
Therefore, the correct choice is D. Choice A is incorrect because the exponent in the denominator should decrease by 1, not increase. Choice B is incorrect because the negative sign is not carried throughout the differentiation. Choice C has an extra power of $c$ and an incorrect exponent in the denominator. Choice E has an incorrect constant factor of $\frac{1}{4}$.

Differentiate the Function B(y)=cy−4B(y)=c y^{-4}B(y)=cy−4 A) B′(y)=5cy4B^{\prime}(y)=\frac{5 c}{y^{4}}B′(y)=y45c​ B) B′(y)=−5cy4B^{\prime}(y)=-\frac{5 c}{y^{4}}B′(y)=−y45c​ C) B′(y)=−4c5yB^{\prime}(y)=-\frac{4 c^{5}}{y}B′(y)=−y4c5​

Differentiate the Function $B(y)=c y^{-4}$ A) $B^{\prime}(y)=\frac{5 c}{y^{4}}$ B) $B^{\prime}(y)=-\frac{5 c}{y^{4}}$ C) $B^{\prime}(y)=-\frac{4 c^{5}}{y}$