Use the product rule to find the derivative?

#f(x)= (6sqrt((x))-2)(5sqrt(x)+7)#

#f(x)= (6sqrt((x))-2)(5sqrt(x)+7)#

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Mar 8, 2018

Answer:

#d/dx(g(x) *h(x)) = g'(x)*h(x)+ h'(x)*g(x)#

Explanation:

Here ,
#g(x) = (6√x−2)#
#h(x) = (5√x+7)#

#g'(x) = 3/sqrt(x)#
#h'(x) = 5/(2*sqrt(x))#

by product rule:

# d/dxf(x) =(6√x−2)*5/(2*sqrt(x)) + (5√x+7)* 3/sqrt(x)#

#=> (3 (5 sqrt(x) + 7))/sqrt(x) + (5 (6 sqrt(x) - 2))/(2 sqrt(x))#

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