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Popular >

derivative of (3x^4-7\times (5x^2+1))

Solution

\frac{d}{d x} ((3 x^{4} - 7) \cdot (5 x^{2} + 1))

Solution

90 x^{5} + 12 x^{3} - 70 x

Solution steps

\frac{d}{d x} ((3 x^{4} - 7) (5 x^{2} + 1))

Apply the Product Rule:

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

f = 3 x^{4} - 7, g = 5 x^{2} + 1

= \frac{d}{d x} (3 x^{4} - 7) (5 x^{2} + 1) + \frac{d}{d x} (5 x^{2} + 1) (3 x^{4} - 7)

\frac{d}{d x} (3 x^{4} - 7) = 12 x^{3}

\frac{d}{d x} (5 x^{2} + 1) = 10 x

= 12 x^{3} (5 x^{2} + 1) + 10 x (3 x^{4} - 7)

Simplify

12 x^{3} (5 x^{2} + 1) + 10 x (3 x^{4} - 7) : 90 x^{5} + 12 x^{3} - 70 x

= 90 x^{5} + 12 x^{3} - 70 x

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Frequently Asked Questions (FAQ)

What is the derivative of (3x^4-7\times (5x^2+1)) ?
The derivative of (3x^4-7\times (5x^2+1)) is 90x^5+12x^3-70x
What is the first derivative of (3x^4-7\times (5x^2+1)) ?
The first derivative of (3x^4-7\times (5x^2+1)) is 90x^5+12x^3-70x