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Popular >

derivative of x(4x-5^3)

Solution

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

Solution

(4 x - 5)^{3} + 12 x (4 x - 5)^{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d x}{d x} = 1

\frac{d}{d x} ((4 x - 5)^{3}) = 12 (4 x - 5)^{2}

= 1 \cdot (4 x - 5)^{3} + 12 (4 x - 5)^{2} x

Simplify

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

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Frequently Asked Questions (FAQ)

What is the derivative of x(4x-5^3) ?
The derivative of x(4x-5^3) is (4x-5)^3+12x(4x-5)^2
What is the first derivative of x(4x-5^3) ?
The first derivative of x(4x-5^3) is (4x-5)^3+12x(4x-5)^2