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Popular >

derivative of sqrt(y+x)

Solution

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

Solution

\frac{\frac{d y}{d x} + 1}{2 y + x}

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

= \frac{\frac{d y}{d x} + 1}{2 y + x}

Popular Examples

derivative of cos(pix)(pi)derivative of

cos (π x) (π)

derivative of (x^2-1(x-1))

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

limit as x approaches 1 of 2x^5-7x^4+7

x \to 1 lim (2 x^{5} - 7 x^{4} + 7)

derivative of-(8(1-12x^2)/((4x^2+1)^3))

\frac{d}{d x} (- \frac{8 ( 1 - 12 x ^{2} )}{( 4 x ^{2} + 1 ) ^{3}})

derivative of f(x)=4pir^2 derivative of

f (x) = 4 π r^{2}

Frequently Asked Questions (FAQ)

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