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Popular >

derivative of (x^2+1sqrt(x))

Solution

\frac{d}{d x} ((x^{2} + 1) x)

Solution

\frac{5 x ^{2} + 1}{2 x}

Solution steps

\frac{d}{d x} ((x^{2} + 1) x)

Apply the Product Rule:

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

f = x^{2} + 1, g = x

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

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

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

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

Simplify

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

= \frac{5 x ^{2} + 1}{2 x}

Graph

Popular Examples

derivative of (ax^2+bx+c*e^{-x/2})

\frac{d}{d x} ((a x^{2} + b x + c) \cdot e^{- \frac{x}{2}})

derivative of 4v^4-(12v^3+9v)derivative of

4 v^{4} - (12 v^{3} + 9 v)

(dy)/(dx)=((x-y))/(x+y)

\frac{d y}{d x} = \frac{( x - y )}{x + y}

derivative of 4+4/x

\frac{d}{d x} (4 + \frac{4}{x})

integral of (x^4+3x^2+5)/(x^4)

\int \frac{x ^{4} + 3 x ^{2} + 5}{x ^{4}} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x^2+1sqrt(x)) ?
The derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))
What is the first derivative of (x^2+1sqrt(x)) ?
The first derivative of (x^2+1sqrt(x)) is (5x^2+1)/(2sqrt(x))