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Popular >

derivative of y=(x^2+3)((2x+5)^6)

Solution

derivative of

y = (x^{2} + 3) ((2 x + 5)^{6})

Solution

2 x (2 x + 5)^{6} + 12 (2 x + 5)^{5} (x^{2} + 3)

Solution steps

\frac{d}{d x} ((x^{2} + 3) (2 x + 5)^{6})

Apply the Product Rule:

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

f = x^{2} + 3, g = (2 x + 5)^{6}

= \frac{d}{d x} (x^{2} + 3) (2 x + 5)^{6} + \frac{d}{d x} ((2 x + 5)^{6}) (x^{2} + 3)

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

\frac{d}{d x} ((2 x + 5)^{6}) = 12 (2 x + 5)^{5}

= 2 x (2 x + 5)^{6} + 12 (2 x + 5)^{5} (x^{2} + 3)

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x \to \frac{1}{3} lim (5 x - 7)

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Frequently Asked Questions (FAQ)

What is the derivative of y=(x^2+3)((2x+5)^6) ?
The derivative of y=(x^2+3)((2x+5)^6) is 2x(2x+5)^6+12(2x+5)^5(x^2+3)
What is the first derivative of y=(x^2+3)((2x+5)^6) ?
The first derivative of y=(x^2+3)((2x+5)^6) is 2x(2x+5)^6+12(2x+5)^5(x^2+3)