Can someone help please me solve this differentiation problem? It'd be appreciated.

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1 Answer
Sean
Feb 3, 2018

#g'(pi/2)=7#

#h'(pi/2)=1/5#

Explanation:

.

#g(x)=f(x)sinx#

Using the product rule:

#g'(x)=f(x)cosx+f'(x)sinx#

#g'(pi/2)=f(pi/2)cos(pi/2)+f'(pi/2)sin(pi/2)#

#g'(pi/2)=(-5)(0)+(7)(1)=0+7=7#

#h(x)=cosx/f(x)#

Using the Quotient Rule:

#h'(x)=((f(x))(-sinx)-(cosx)(f'(x)))/(f(x))^2#

#h'(pi/2)=((f(pi/2))(-sin(pi/2)-(cos(pi/2))(f'(pi/2))))/(f(pi/2))^2#

#h'(pi/2)=((-5)(-1)-(0)(7))/(-5)^2=(5-0)/25=5/25=1/5#

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