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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}

Popular Examples

derivative of (3x^4-18x^5*cos(5x^2))

\frac{d}{d x} ((3 x^{4} - 18 x)^{5} \cdot cos (5 x^{2}))

integral of (2x^2+3)^2

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

(yx-y)dy-(y+1)dx=0

(y x - y) d y - (y + 1) d x = 0

integral of e^{-x}*sin(2x)

\int e^{- x} \cdot sin (2 x) d x

integral of (arctan(x)-ln(x))

\int (arctan (x) - ln (x)) 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))