How do you find the derivative of #f(x)=5x^3+12x^2-15#?

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Answer 1 · 2018-07-12T21:50:52

#f'(x)=15x^2+24x#

Given function:

#f(x)=5x^3+12x^2-15#

differentiating above function w.r.t. #x# as follows

#\frac{d}{dx}f(x)=\frac{d}{dx}(5x^3+12x^2-15)#

#f'(x)=\frac{d}{dx}(5x^3)+\frac{d}{dx}(12x^2)-\frac{d}{dx}(15)#

#=5\frac{d}{dx}(x^3)+12\frac{d}{dx}(x^2)-0#

#=5(3x^2)+12(2x)#

#=15x^2+24x#

Answer 2 · 2018-07-12T21:53:47

#f'(x)=15x^2+24x#

Whenever we're trying to differentiate a polynomial, it helps to use the power rule.

In essence, with the power rule, the exponent becomes the coefficient, and the power is decremented by one. We get

#f'(x)=15x^2+24x#

Recall that the derivative of a constant is zero.

Hope this helps!