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

Given function:

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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

Recall that the derivative of a constant is zero.

Hope this helps!

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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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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.

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.

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.

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