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\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\cdot\left(1+2x\right)}=2x\right)

Find the derivative of x(1+y)^0.5+(y(1+2x))^0.5=2x

Answer

$\frac{\sqrt{y}}{\sqrt{2x+1}}+\sqrt{y+1}=2$

Step-by-step explanation

Problem

$\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\cdot\left(1+2x\right)}=2x\right)$
1

The power of a product is equal to the product of it's factors raised to the same power

$\frac{d}{dx}\left(\sqrt{2x+1}\sqrt{y}+\sqrt{y+1}x=2x\right)$

Unlock this step-by-step solution!

Answer

$\frac{\sqrt{y}}{\sqrt{2x+1}}+\sqrt{y+1}=2$
$\frac{d}{dx}\left(x\sqrt{1+y}+\sqrt{y\cdot\left(1+2x\right)}=2x\right)$

Main topic:

Differential calculus

Used formulas:

4. See formulas

Time to solve it:

~ 0.35 seconds