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Popular Calculus >

derivative of y=x^3(2x-5)^4

Solution

derivative of

y = x^{3} (2 x - 5)^{4}

Solution

3 x^{2} (2 x - 5)^{4} + 8 (2 x - 5)^{3} x^{3}

Solution steps

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

Apply the Product Rule:

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

f = x^{3}, g = (2 x - 5)^{4}

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

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

\frac{d}{d x} ((2 x - 5)^{4}) = 8 (2 x - 5)^{3}

= 3 x^{2} (2 x - 5)^{4} + 8 (2 x - 5)^{3} x^{3}

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=x^3(2x-5)^4 ?
The derivative of y=x^3(2x-5)^4 is 3x^2(2x-5)^4+8(2x-5)^3x^3
What is the first derivative of y=x^3(2x-5)^4 ?
The first derivative of y=x^3(2x-5)^4 is 3x^2(2x-5)^4+8(2x-5)^3x^3