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Popular >

derivative of (3sqrt(x)+7)x^2

Solution

derivative of

(3 x + 7) x^{2}

Solution

\frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 7)

Solution steps

\frac{d}{d x} ((3 x + 7) x^{2})

Apply the Product Rule:

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

f = 3 x + 7, g = x^{2}

= \frac{d}{d x} (3 x + 7) x^{2} + \frac{d}{d x} (x^{2}) (3 x + 7)

\frac{d}{d x} (3 x + 7) = \frac{3}{2 x}

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

= \frac{3}{2 x} x^{2} + 2 x (3 x + 7)

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

= \frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 7)

Popular Examples

derivative of-(32/(x^3)+4/(x^2))

\frac{d}{d x} (- \frac{32}{x ^{3}} + \frac{4}{x ^{2}})

integral from 2 to 4 of (x^2+1)/(x^2-5)

\int_{2}^{4} \frac{x ^{2} + 1}{x ^{2} - 5} d x

integral of x^3cos(x^2)

\int x^{3} cos (x^{2}) d x

integral of xsqrt(x-9)

\int x x - 9 d x

tangent of 3xy^3+4xy=28,(4,1)tangent of

3 x y^{3} + 4 x y = 28, (4, 1)

Frequently Asked Questions (FAQ)

What is the derivative of (3sqrt(x)+7)x^2 ?
The derivative of (3sqrt(x)+7)x^2 is (3x^{3/2})/2+2x(3sqrt(x)+7)
What is the first derivative of (3sqrt(x)+7)x^2 ?
The first derivative of (3sqrt(x)+7)x^2 is (3x^{3/2})/2+2x(3sqrt(x)+7)