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Popular >

derivative of (9+4x-6sqrt(x)/x)

Solution

\frac{d}{d x} (\frac{9 + 4 x - 6 x}{x})

Solution

\frac{3 x - 9}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{9 + 4 x - 6 x}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 9 + 4 x - 6 x ) x - \frac{d x}{d x} ( 9 + 4 x - 6 x )}{x ^{2}}

\frac{d}{d x} (9 + 4 x - 6 x) = - \frac{3}{x} + 4

\frac{d x}{d x} = 1

= \frac{( - \frac{3}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 6 x )}{x ^{2}}

Simplify

\frac{( - \frac{3}{x} + 4 ) x - 1 \cdot ( 9 + 4 x - 6 x )}{x ^{2}} : \frac{3 x - 9}{x ^{2}}

= \frac{3 x - 9}{x ^{2}}

Graph

Popular Examples

(\partial)/(\partial x)(ln(x*cos(y)))

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

integral of 1/((x^2-441)^{3/2)}

\int \frac{1}{( x ^{2} - 441 ) ^{\frac{3}{2}}} d x

derivative of \sqrt[3]{(3x^2+5x-1^2})

\frac{d}{d x} (3 (3 x^{2} + 5 x - 1)^{2})

y^{''}-2y^'+5y=e^{-2t}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{- 2 t}

inverse oflaplace (2s-6)/(s^2+9)inverse laplace

\frac{2 s - 6}{s ^{2} + 9}

Frequently Asked Questions (FAQ)

What is the derivative of (9+4x-6sqrt(x)/x) ?
The derivative of (9+4x-6sqrt(x)/x) is (3sqrt(x)-9)/(x^2)
What is the first derivative of (9+4x-6sqrt(x)/x) ?
The first derivative of (9+4x-6sqrt(x)/x) is (3sqrt(x)-9)/(x^2)