What is the derivative of x(2x+1)^4 ?

The derivative of x(2x+1)^4 is (2x+1)^4+8x(2x+1)^3

What is the first derivative of x(2x+1)^4 ?

The first derivative of x(2x+1)^4 is (2x+1)^4+8x(2x+1)^3

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derivative of

x (2 x + 1)^{4}

(2 x + 1)^{4} + 8 x (2 x + 1)^{3}

Solution steps

\frac{d}{d x} (x (2 x + 1)^{4})

Apply the Product Rule:

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

f = x, g = (2 x + 1)^{4}

= \frac{d x}{d x} (2 x + 1)^{4} + \frac{d}{d x} ((2 x + 1)^{4}) x

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

\frac{d}{d x} ((2 x + 1)^{4}) = 8 (2 x + 1)^{3}

= 1 \cdot (2 x + 1)^{4} + 8 (2 x + 1)^{3} x

Simplify

= (2 x + 1)^{4} + 8 x (2 x + 1)^{3}

\frac{d}{d x} (e^{x} cos (y))

\int cos^{2} (x) + 2 cos (x) + 1 d x

\int (x^{\frac{3}{4}}) d x

\int \frac{x ^{2} + 1}{x ^{3} + x ^{2}} d x

y e^{x}

What is the derivative of x(2x+1)^4 ?
The derivative of x(2x+1)^4 is (2x+1)^4+8x(2x+1)^3
What is the first derivative of x(2x+1)^4 ?
The first derivative of x(2x+1)^4 is (2x+1)^4+8x(2x+1)^3