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Popular >

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

Solution

\frac{d}{d x} ((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

Popular Examples

derivative of y=8-6(x-1)derivative of

y = 8 - 6 (x - 1)

derivative of (x^2+5x^3)

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

f (x) = ln (3 x + 1)

integral of (x^3-2x^2)(1/x-5)

\int (x^{3} - 2 x^{2}) (\frac{1}{x} - 5) d x

limit as x approaches 2-of ln(2-x)

x \to 2 - lim (ln (2 - x))

Frequently Asked Questions (FAQ)

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