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Popular Calculus >

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

Solution

derivative of

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

Solution

\frac{5 x x + 9 x}{2}

Solution steps

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

Apply the Product Rule:

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

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

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

\frac{d}{d x} (x) = \frac{1}{2 x}

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

= \frac{1}{2 x} (3 x + x^{2}) + (3 + 2 x) x

Simplify

\frac{1}{2 x} (3 x + x^{2}) + (3 + 2 x) x : \frac{5 x x + 9 x}{2}

= \frac{5 x x + 9 x}{2}

Graph

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Frequently Asked Questions (FAQ)

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