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Popular >

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

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

Popular Examples

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derivative of 2x-(2000/(x^2))

\frac{d}{d x} (2 x - \frac{2000}{x ^{2}})

Frequently Asked Questions (FAQ)

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