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Popular >

derivative of (3sqrt(x)+8x^2)

Solution

\frac{d}{d x} ((3 x + 8) x^{2})

Solution

\frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 8)

Solution steps

\frac{d}{d x} ((3 x + 8) x^{2})

Apply the Product Rule:

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

f = 3 x + 8, g = x^{2}

= \frac{d}{d x} (3 x + 8) x^{2} + \frac{d}{d x} (x^{2}) (3 x + 8)

\frac{d}{d x} (3 x + 8) = \frac{3}{2 x}

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

= \frac{3}{2 x} x^{2} + 2 x (3 x + 8)

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

= \frac{3 x ^{\frac{3}{2}}}{2} + 2 x (3 x + 8)

Graph

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\int_{0}^{4} x (x + 2) d x

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\int_{0}^{1} 6 cos (4 x) d x

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Frequently Asked Questions (FAQ)

What is the derivative of (3sqrt(x)+8x^2) ?
The derivative of (3sqrt(x)+8x^2) is (3x^{3/2})/2+2x(3sqrt(x)+8)
What is the first derivative of (3sqrt(x)+8x^2) ?
The first derivative of (3sqrt(x)+8x^2) is (3x^{3/2})/2+2x(3sqrt(x)+8)