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Popular >

derivative of y=(3sqrt(x)+2)x^2

Solution

derivative of

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

Solution

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

Solution steps

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

Apply the Product Rule:

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

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

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

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

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

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

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

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

Popular Examples

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Frequently Asked Questions (FAQ)

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