What is the derivative of y=x^3(2x-1)^7 ?

The derivative of y=x^3(2x-1)^7 is 3x^2(2x-1)^7+14(2x-1)^6x^3

What is the first derivative of y=x^3(2x-1)^7 ?

The first derivative of y=x^3(2x-1)^7 is 3x^2(2x-1)^7+14(2x-1)^6x^3

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derivative of

y = x^{3} (2 x - 1)^{7}

3 x^{2} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{3}

Solution steps

\frac{d}{d x} (x^{3} (2 x - 1)^{7})

Apply the Product Rule:

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

f = x^{3}, g = (2 x - 1)^{7}

= \frac{d}{d x} (x^{3}) (2 x - 1)^{7} + \frac{d}{d x} ((2 x - 1)^{7}) x^{3}

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

\frac{d}{d x} ((2 x - 1)^{7}) = 14 (2 x - 1)^{6}

= 3 x^{2} (2 x - 1)^{7} + 14 (2 x - 1)^{6} x^{3}

What is the derivative of y=x^3(2x-1)^7 ?
The derivative of y=x^3(2x-1)^7 is 3x^2(2x-1)^7+14(2x-1)^6x^3
What is the first derivative of y=x^3(2x-1)^7 ?
The first derivative of y=x^3(2x-1)^7 is 3x^2(2x-1)^7+14(2x-1)^6x^3