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Popular >

derivative of (4x^2-1(7x^3+x))

Solution

\frac{d}{d x} ((4 x^{2} - 1) (7 x^{3} + x))

Solution

140 x^{4} - 9 x^{2} - 1

Solution steps

\frac{d}{d x} ((4 x^{2} - 1) (7 x^{3} + x))

Apply the Product Rule:

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

f = 4 x^{2} - 1, g = 7 x^{3} + x

= \frac{d}{d x} (4 x^{2} - 1) (7 x^{3} + x) + \frac{d}{d x} (7 x^{3} + x) (4 x^{2} - 1)

\frac{d}{d x} (4 x^{2} - 1) = 8 x

\frac{d}{d x} (7 x^{3} + x) = 21 x^{2} + 1

= 8 x (7 x^{3} + x) + (21 x^{2} + 1) (4 x^{2} - 1)

Simplify

8 x (7 x^{3} + x) + (21 x^{2} + 1) (4 x^{2} - 1) : 140 x^{4} - 9 x^{2} - 1

= 140 x^{4} - 9 x^{2} - 1

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Frequently Asked Questions (FAQ)

What is the derivative of (4x^2-1(7x^3+x)) ?
The derivative of (4x^2-1(7x^3+x)) is 140x^4-9x^2-1
What is the first derivative of (4x^2-1(7x^3+x)) ?
The first derivative of (4x^2-1(7x^3+x)) is 140x^4-9x^2-1