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Popular >

derivative of (4^{x^3}+2^3)

Solution

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

Solution

9 ln (2) \cdot 2^{2 x^{3} + 1} x^{2} (4^{x^{3}} + 2)^{2}

Solution steps

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

Apply the chain rule:

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

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

\frac{d}{d x} (4^{x^{3}} + 2) = 3 ln (2) \cdot 2^{2 x^{3} + 1} x^{2}

= 3 (4^{x^{3}} + 2)^{2} \cdot 3 ln (2) \cdot 2^{2 x^{3} + 1} x^{2}

Simplify

= 9 ln (2) \cdot 2^{2 x^{3} + 1} x^{2} (4^{x^{3}} + 2)^{2}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (4^{x^3}+2^3) ?
The derivative of (4^{x^3}+2^3) is 9ln(2)*2^{2x^3+1}x^2(4^{x^3}+2)^2
What is the first derivative of (4^{x^3}+2^3) ?
The first derivative of (4^{x^3}+2^3) is 9ln(2)*2^{2x^3+1}x^2(4^{x^3}+2)^2