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Popular >

derivative of y=sqrt(x+\sqrt{x)}

Solution

derivative of

y = x + x

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 x + x} (1 + \frac{1}{2 x}) : \frac{2 x + 1}{4 x x + x}

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

Popular Examples

limit as x approaches 0+of (-7x)ln(6x^4)

x \to 0 + lim ((- 7 x) ln (6 x^{4}))

integral of 1/(sqrt(3x)+1)

\int \frac{1}{3 x + 1} d x

derivative of ln(x^6)derivative of

ln (x^{6})

sum from n=0 to infinity}(4^{(2n+1) of)/((-4)^n)

n = 0 \sum \infty \frac{4 ^{(2 n + 1)}}{( - 4 ) ^{n}}

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

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

Frequently Asked Questions (FAQ)

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