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Popular >

derivative of (3x-4(x^3+5))

Solution

\frac{d}{d x} ((3 x - 4) (x^{3} + 5))

Solution

12 x^{3} - 12 x^{2} + 15

Solution steps

\frac{d}{d x} ((3 x - 4) (x^{3} + 5))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = 3 x - 4, g = x^{3} + 5

= \frac{d}{d x} (3 x - 4) (x^{3} + 5) + \frac{d}{d x} (x^{3} + 5) (3 x - 4)

\frac{d}{d x} (3 x - 4) = 3

\frac{d}{d x} (x^{3} + 5) = 3 x^{2}

= 3 (x^{3} + 5) + 3 x^{2} (3 x - 4)

Simplify

3 (x^{3} + 5) + 3 x^{2} (3 x - 4) : 12 x^{3} - 12 x^{2} + 15

= 12 x^{3} - 12 x^{2} + 15

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Frequently Asked Questions (FAQ)

What is the derivative of (3x-4(x^3+5)) ?
The derivative of (3x-4(x^3+5)) is 12x^3-12x^2+15
What is the first derivative of (3x-4(x^3+5)) ?
The first derivative of (3x-4(x^3+5)) is 12x^3-12x^2+15