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Popular >

derivative of sqrt(x\sqrt{x+1)}

Solution

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

Solution

\frac{3 x + 2}{4 x x + 1 x + 1}

Solution steps

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

Apply the chain rule:

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

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

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

= \frac{1}{2 x x + 1} \cdot \frac{3 x + 2}{2 x + 1}

Simplify

\frac{1}{2 x x + 1} \cdot \frac{3 x + 2}{2 x + 1} : \frac{3 x + 2}{4 x x + 1 x + 1}

= \frac{3 x + 2}{4 x x + 1 x + 1}

Popular Examples

integral of (x^2+5)cos(3x)

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

derivative of f(x)=x^3cos(2x)derivative of

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

x(dy)/(dx)=x^3+9x^3y

x \frac{d y}{d x} = x^{3} + 9 x^{3} y

y^{''}=6x,y(0)=1,y^'(0)=-1

y^{^{''}} = 6 x, y (0) = 1, y^{^{'}} (0) = - 1

integral of 1/(sqrt(49-64x^2))

\int \frac{1}{49 - 64 x ^{2}} d x

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(x\sqrt{x+1)} ?
The derivative of sqrt(x\sqrt{x+1)} is (3x+2)/(4sqrt(x\sqrt{x+1))sqrt(x+1)}
What is the first derivative of sqrt(x\sqrt{x+1)} ?
The first derivative of sqrt(x\sqrt{x+1)} is (3x+2)/(4sqrt(x\sqrt{x+1))sqrt(x+1)}