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Popular Calculus >

derivative of (4x+9/(sqrt(x)))

Solution

\frac{d}{d x} (\frac{4 x + 9}{x})

Solution

\frac{4 x - 9}{2 x x}

Solution steps

\frac{d}{d x} (\frac{4 x + 9}{x})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( 4 x + 9 ) x - \frac{d}{d x} ( x ) ( 4 x + 9 )}{( x ) ^{2}}

\frac{d}{d x} (4 x + 9) = 4

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

= \frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}}

Simplify

\frac{4 x - \frac{1}{2 x} ( 4 x + 9 )}{( x ) ^{2}} : \frac{4 x - 9}{2 x x}

= \frac{4 x - 9}{2 x x}

Graph

Popular Examples

integral of (x-1)/(x+1)

\int \frac{x - 1}{x + 1} d x

derivative of 2(x^2+5x-2^{-5/7})

\frac{d}{d x} (2 (x^{2} + 5 x - 2)^{- \frac{5}{7}})

(d^2y)/(dt^2)+9y=0

\frac{d ^{2} y}{d t ^{2}} + 9 y = 0

derivative of csc^2(x-2)

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

(\partial)/(\partial x)(x^{0.4}y^{0.6})

\frac{\partial}{\partial x} (x^{0.4} y^{0.6})

Frequently Asked Questions (FAQ)

What is the derivative of (4x+9/(sqrt(x))) ?
The derivative of (4x+9/(sqrt(x))) is (4x-9)/(2xsqrt(x))
What is the first derivative of (4x+9/(sqrt(x))) ?
The first derivative of (4x+9/(sqrt(x))) is (4x-9)/(2xsqrt(x))