How do you find the derivative of f(x) = x²(3x³-1) and the given point is (1,2)?

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Answer 1 · 2018-02-21T13:05:34

13

#f'(x) = d/(dx) f(x)#

#= d/dx x^2(3x^3 -1)# #color(white)(dwwwwwdd# #["applying product rule"]#

#= (d/dx x^2)(3x^3 -1) + x^2(d/dx 3x^3 - d/dx 1)#

#= 2x(3x^3 - 1) + x^2(9x^2)#

#= 6x^4 - 2x + 9x^4#

#= 15x^4 - 2x#

So, Derivative of f(x) at (1, 2) = #f'(1) = 15(1)^4 - 2*1 = 15 - 2 = 13# #color(white)(dwww#(just replace #x=1#)

Hence Explained.