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Popular >

derivative of sqrt(3x+2y)

Solution

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

Solution

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

Solution steps

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

Apply the chain rule:

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

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

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

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

Simplify

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

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

Popular Examples

limit as x approaches 2 of (2-x)/(x^2-4)

x \to 2 lim (\frac{2 - x}{x ^{2} - 4})

(\partial)/(\partial x)(1/(x+y^2))

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

(\partial)/(\partial y)((x^3-y^2)^{-1})

\frac{\partial}{\partial y} ((x^{3} - y^{2})^{- 1})

integral of (x+1)5^{(x+1)^2}

\int (x + 1) 5^{(x + 1)^{2}} d x

derivative of e^x-3x^2

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

Frequently Asked Questions (FAQ)

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