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!

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