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Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

derivative of ((x^3-1/(2x^3+1))^4)

\frac{d}{d x} ((\frac{x ^{3} - 1}{2 x ^{3} + 1})^{4})

(\partial)/(\partial x)(2^{xy})

\frac{\partial}{\partial x} (2^{x y})

derivative of f(x)= 2/((1-x)^3)derivative of

f (x) = \frac{2}{( 1 - x ) ^{3}}

(\partial}{\partial x}(e^{\frac{x^2)/2})

\frac{\partial}{\partial x} (e^{\frac{x ^{2}}{2}})

tangent of f(x)=(-8x)/(x^2+1),(1,-4)tangent of

f (x) = \frac{- 8 x}{x ^{2} + 1}, (1, - 4)

Frequently Asked Questions (FAQ)

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