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Popular >

derivative of x^2sqrt(3x+5)

Solution

derivative of

x^{2} 3 x + 5

Solution

\frac{15 x ^{2} + 20 x}{2 3 x + 5}

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

= 2 x 3 x + 5 + \frac{3}{2 3 x + 5} x^{2}

Simplify

2 x 3 x + 5 + \frac{3}{2 3 x + 5} x^{2} : \frac{15 x ^{2} + 20 x}{2 3 x + 5}

= \frac{15 x ^{2} + 20 x}{2 3 x + 5}

Popular Examples

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\int \frac{x}{( x ^{2} + 7 ) ^{2}} d x

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x \to - 1 lim (arccos (x))

integral from 0 to pi of 3sin^2(xco)s^4x

\int_{0}^{π} 3 sin^{2} (x co) s^{4} x d x

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

Frequently Asked Questions (FAQ)

What is the derivative of x^2sqrt(3x+5) ?
The derivative of x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))
What is the first derivative of x^2sqrt(3x+5) ?
The first derivative of x^2sqrt(3x+5) is (15x^2+20x)/(2sqrt(3x+5))