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Popular >

derivative of f(x)=(11sqrt(x)+2)x^2

Solution

derivative of

f (x) = (11 x + 2) x^{2}

Solution

\frac{11 x ^{\frac{3}{2}}}{2} + 2 x (11 x + 2)

Solution steps

\frac{d}{d x} ((11 x + 2) x^{2})

Apply the Product Rule:

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

f = 11 x + 2, g = x^{2}

= \frac{d}{d x} (11 x + 2) x^{2} + \frac{d}{d x} (x^{2}) (11 x + 2)

\frac{d}{d x} (11 x + 2) = \frac{11}{2 x}

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

= \frac{11}{2 x} x^{2} + 2 x (11 x + 2)

\frac{11}{2 x} x^{2} = \frac{11 x ^{\frac{3}{2}}}{2}

= \frac{11 x ^{\frac{3}{2}}}{2} + 2 x (11 x + 2)

Graph

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Frequently Asked Questions (FAQ)

What is the derivative of f(x)=(11sqrt(x)+2)x^2 ?
The derivative of f(x)=(11sqrt(x)+2)x^2 is (11x^{3/2})/2+2x(11sqrt(x)+2)
What is the first derivative of f(x)=(11sqrt(x)+2)x^2 ?
The first derivative of f(x)=(11sqrt(x)+2)x^2 is (11x^{3/2})/2+2x(11sqrt(x)+2)