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Popular >

derivative of xsqrt(x+1)

Solution

derivative of

x x + 1

Solution

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

Solution steps

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

Apply the Product Rule:

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

f = x, g = x + 1

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

\frac{d x}{d x} = 1

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

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

Simplify

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

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

Popular Examples

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(1, - 6), (- 3, 4)

derivative of x^3+y^3=6xy derivative of

x^{3} + y^{3} = 6 x y

tangent of y=sqrt(x),(1,1)tangent of

y = x, (1, 1)

cartesian (2,(3pi)/4)polar to cartesian

(2, \frac{3 π}{4})

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

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

Frequently Asked Questions (FAQ)

What is the derivative of xsqrt(x+1) ?
The derivative of xsqrt(x+1) is (3x+2)/(2sqrt(x+1))
What is the first derivative of xsqrt(x+1) ?
The first derivative of xsqrt(x+1) is (3x+2)/(2sqrt(x+1))