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Popular Calculus >

derivative of 40x(5x^2-8)

Solution

\frac{d}{d x} (40 x (5 x^{2} - 8))

Solution

40 (15 x^{2} - 8)

Solution steps

\frac{d}{d x} (40 x (5 x^{2} - 8))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= 40 \frac{d}{d x} (x (5 x^{2} - 8))

Apply the Product Rule:

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

f = x, g = 5 x^{2} - 8

= 40 (\frac{d x}{d x} (5 x^{2} - 8) + \frac{d}{d x} (5 x^{2} - 8) x)

\frac{d x}{d x} = 1

\frac{d}{d x} (5 x^{2} - 8) = 10 x

= 40 (1 \cdot (5 x^{2} - 8) + 10 xx)

Simplify

40 (1 \cdot (5 x^{2} - 8) + 10 xx) : 40 (15 x^{2} - 8)

= 40 (15 x^{2} - 8)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of 40x(5x^2-8) ?
The derivative of 40x(5x^2-8) is 40(15x^2-8)
What is the first derivative of 40x(5x^2-8) ?
The first derivative of 40x(5x^2-8) is 40(15x^2-8)