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Popular >

derivative of y=(9sqrt(x)+5)x^2

Solution

derivative of

y = (9 x + 5) x^{2}

Solution

\frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)

Solution steps

\frac{d}{d x} ((9 x + 5) x^{2})

Apply the Product Rule:

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

f = 9 x + 5, g = x^{2}

= \frac{d}{d x} (9 x + 5) x^{2} + \frac{d}{d x} (x^{2}) (9 x + 5)

\frac{d}{d x} (9 x + 5) = \frac{9}{2 x}

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

= \frac{9}{2 x} x^{2} + 2 x (9 x + 5)

\frac{9}{2 x} x^{2} = \frac{9 x ^{\frac{3}{2}}}{2}

= \frac{9 x ^{\frac{3}{2}}}{2} + 2 x (9 x + 5)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of y=(9sqrt(x)+5)x^2 ?
The derivative of y=(9sqrt(x)+5)x^2 is (9x^{3/2})/2+2x(9sqrt(x)+5)
What is the first derivative of y=(9sqrt(x)+5)x^2 ?
The first derivative of y=(9sqrt(x)+5)x^2 is (9x^{3/2})/2+2x(9sqrt(x)+5)