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Popular >

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

Solution

derivative of

y = (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

Popular Examples

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implicit (dy)/(dx),xy=9 implicit derivative

\frac{d y}{d x}, x y = 9

(dy)/(7a+y)=dxcot(x)

\frac{d y}{7 a + y} = d x cot (x)

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y = 7 + 2 x, y = \frac{14 + x}{2}

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

Frequently Asked Questions (FAQ)

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