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Popular >

derivative of sqrt(2x+3y)

Solution

\frac{d}{d x} (2 x + 3 y)

Solution

\frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}

Solution steps

\frac{d}{d x} (2 x + 3 y)

Apply the chain rule:

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

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

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

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

Simplify

\frac{1}{2 2 x + 3 y} (2 + 3 \frac{d y}{d x}) : \frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}

= \frac{2 + 3 \frac{d y}{d x}}{2 2 x + 3 y}

Popular Examples

limit as x approaches 2pi of (sin(x))/x

x \to 2 π lim (\frac{sin ( x )}{x})

(\partial)/(\partial y)(xln(xy))

\frac{\partial}{\partial y} (x ln (x y))

sum from n=1 to infinity of (cos(npi))/n

n = 1 \sum \infty \frac{cos ( nπ )}{n}

limit as t approaches 0 of (e^{-1t}-1)/t

t \to 0 lim (\frac{e ^{- 1 t} - 1}{t})

implicit (dy)/(dx),-x/y =0 implicit derivative

\frac{d y}{d x}, - \frac{x}{y} = 0

Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2x+3y) ?
The derivative of sqrt(2x+3y) is (2+3\frac{dy)/(dx)}{2sqrt(2x+3y)}
What is the first derivative of sqrt(2x+3y) ?
The first derivative of sqrt(2x+3y) is (2+3\frac{dy)/(dx)}{2sqrt(2x+3y)}