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Popular >

derivative of y=x(6x+1)^5

Solution

derivative of

y = x (6 x + 1)^{5}

Solution

(6 x + 1)^{5} + 30 x (6 x + 1)^{4}

Solution steps

\frac{d}{d x} (x (6 x + 1)^{5})

Apply the Product Rule:

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

f = x, g = (6 x + 1)^{5}

= \frac{d x}{d x} (6 x + 1)^{5} + \frac{d}{d x} ((6 x + 1)^{5}) x

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

\frac{d}{d x} ((6 x + 1)^{5}) = 30 (6 x + 1)^{4}

= 1 \cdot (6 x + 1)^{5} + 30 (6 x + 1)^{4} x

Simplify

= (6 x + 1)^{5} + 30 x (6 x + 1)^{4}

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Frequently Asked Questions (FAQ)

What is the derivative of y=x(6x+1)^5 ?
The derivative of y=x(6x+1)^5 is (6x+1)^5+30x(6x+1)^4
What is the first derivative of y=x(6x+1)^5 ?
The first derivative of y=x(6x+1)^5 is (6x+1)^5+30x(6x+1)^4