What is the derivative of x(2x+1^5) ?

The derivative of x(2x+1^5) is (2x+1)^5+10x(2x+1)^4

What is the first derivative of x(2x+1^5) ?

The first derivative of x(2x+1^5) is (2x+1)^5+10x(2x+1)^4

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\frac{d}{d x} (x (2 x + 1)^{5})

(2 x + 1)^{5} + 10 x (2 x + 1)^{4}

Solution steps

\frac{d}{d x} (x (2 x + 1)^{5})

Apply the Product Rule:

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

f = x, g = (2 x + 1)^{5}

= \frac{d x}{d x} (2 x + 1)^{5} + \frac{d}{d x} ((2 x + 1)^{5}) x

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

\frac{d}{d x} ((2 x + 1)^{5}) = 10 (2 x + 1)^{4}

= 1 \cdot (2 x + 1)^{5} + 10 (2 x + 1)^{4} x

Simplify

= (2 x + 1)^{5} + 10 x (2 x + 1)^{4}

What is the derivative of x(2x+1^5) ?
The derivative of x(2x+1^5) is (2x+1)^5+10x(2x+1)^4
What is the first derivative of x(2x+1^5) ?
The first derivative of x(2x+1^5) is (2x+1)^5+10x(2x+1)^4