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Popular >

derivative of (1+2x^{1/2})

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

laplacetransform t+3 laplace transform

t + 3

integral of 10x-3

\int 10 x - 3 d x

area y= 1/x ,y=x,y= x/4 area

y = \frac{1}{x}, y = x, y = \frac{x}{4}

(dy)/(dx)=1-cos(2x-y+3)

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

derivative of f(x)= 8/(x^3)derivative of

f (x) = \frac{8}{x ^{3}}

Frequently Asked Questions (FAQ)

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