Can I get help with this derivatives/differentiation problem please?

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Answer 1 · 2018-02-03T01:45:43

#g'(x) = d/dx x^2f(x) = 2xf(x) +x^2f'(x)#

so:

#g'(5) = 2*5*5+5^2*5 = 175#

The tangent line to #g(x)# for #x=5# has the equation:

#y= g(5)+g'(5)(x-5)#

#y= 125 + 175(x-5)#

#y= 175x -750#

#h'(x) = d/dx (f(x))/(x-6) = (f'(x)(x-6)-f(x))/(x-6)^2#

#h'(5) = (5*(-1) - 5)/(-1)^2 = -10#

The tangent line to #h(x)# for #x=5# has the equation:

#y= h(5)+h'(5)(x-5)#

#y = -5 -10(x-5)#

#y= -10x +45#