What is the derivative of x(2x+3^4) ?

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

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

Simplify

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

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