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Popular Calculus >

derivative of (8x^3-5x+2)^pi

Solution

derivative of

(8 x^{3} - 5 x + 2)^{π}

Solution

π (8 x^{3} - 5 x + 2)^{π - 1} (24 x^{2} - 5)

Solution steps

\frac{d}{d x} ((8 x^{3} - 5 x + 2)^{π})

Apply the chain rule:

π (8 x^{3} - 5 x + 2)^{π - 1} \frac{d}{d x} (8 x^{3} - 5 x + 2)

= π (8 x^{3} - 5 x + 2)^{π - 1} \frac{d}{d x} (8 x^{3} - 5 x + 2)

\frac{d}{d x} (8 x^{3} - 5 x + 2) = 24 x^{2} - 5

= π (8 x^{3} - 5 x + 2)^{π - 1} (24 x^{2} - 5)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of (8x^3-5x+2)^pi ?
The derivative of (8x^3-5x+2)^pi is pi(8x^3-5x+2)^{pi-1}(24x^2-5)
What is the first derivative of (8x^3-5x+2)^pi ?
The first derivative of (8x^3-5x+2)^pi is pi(8x^3-5x+2)^{pi-1}(24x^2-5)