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

Answer 1

Charles Anctil

#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#

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Answer 2

Emilia Aguilar

#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!

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Answer 3

Christopher Allers

To find the derivative of ( f(x) = 5x^3 + 12x^2 - 15 ), you apply the power rule for derivatives, which states that the derivative of ( x^n ) with respect to ( x ) is ( nx^{n-1} ).

So, the derivative of ( 5x^3 ) is ( 15x^{3-1} ), which simplifies to ( 15x^2 ). The derivative of ( 12x^2 ) is ( 24x^{2-1} ), which simplifies to ( 24x ). The derivative of the constant term ( -15 ) is ( 0 ) since the derivative of any constant is zero.

Therefore, the derivative of ( f(x) = 5x^3 + 12x^2 - 15 ) is ( f'(x) = 15x^2 + 24x ).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.