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Popular Calculus >

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

derivative of sqrt(25+x^2)

\frac{d}{d x} (25 + x^{2})

slope of (2,-2),(9,3)

s l o p e (2, - 2), (9, 3)

derivative of 4arcsin(x^2)

d er i v a t i v e 4 arcsin (x^{2})

derivative of Ate^{-t}

\frac{d}{d x} (A t e^{- t})

(\partial)/(\partial y)(3y^2)

\frac{\partial}{\partial y} (3 y^{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)}