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Popular >

derivative of (x^2+3(x^2-2)^8)

Solution

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 2)^{8})

Solution

2 x (x^{2} - 2)^{8} + 16 x (x^{2} - 2)^{7} (x^{2} + 3)

Solution steps

\frac{d}{d x} ((x^{2} + 3) (x^{2} - 2)^{8})

Apply the Product Rule:

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

f = x^{2} + 3, g = (x^{2} - 2)^{8}

= \frac{d}{d x} (x^{2} + 3) (x^{2} - 2)^{8} + \frac{d}{d x} ((x^{2} - 2)^{8}) (x^{2} + 3)

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

\frac{d}{d x} ((x^{2} - 2)^{8}) = 16 x (x^{2} - 2)^{7}

= 2 x (x^{2} - 2)^{8} + 16 x (x^{2} - 2)^{7} (x^{2} + 3)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (x^2+3(x^2-2)^8) ?
The derivative of (x^2+3(x^2-2)^8) is 2x(x^2-2)^8+16x(x^2-2)^7(x^2+3)
What is the first derivative of (x^2+3(x^2-2)^8) ?
The first derivative of (x^2+3(x^2-2)^8) is 2x(x^2-2)^8+16x(x^2-2)^7(x^2+3)