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Popular >

derivative of y=(3+5x-8sqrt(x))/x

Solution

derivative of

y = \frac{3 + 5 x - 8 x}{x}

Solution

\frac{4 x - 3}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 + 5 x - 8 x}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 3 + 5 x - 8 x ) x - \frac{d x}{d x} ( 3 + 5 x - 8 x )}{x ^{2}}

\frac{d}{d x} (3 + 5 x - 8 x) = - \frac{4}{x} + 5

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

= \frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}}

Simplify

\frac{( - \frac{4}{x} + 5 ) x - 1 \cdot ( 3 + 5 x - 8 x )}{x ^{2}} : \frac{4 x - 3}{x ^{2}}

= \frac{4 x - 3}{x ^{2}}

Popular Examples

(\partial)/(\partial y)(e^{2x}+yln(x))

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

(\partial)/(\partial x)(xarctan(y/z))

\frac{\partial}{\partial x} (x arctan (\frac{y}{z}))

derivative of (e^{3x}/(x^{15)})

\frac{d}{d x} (\frac{e ^{3 x}}{x ^{15}})

area y=2x+1,y=13-x^2,x=-1,x=2 area

y = 2 x + 1, y = 13 - x^{2}, x = - 1, x = 2

integral of (ln(9x))/x

\int \frac{ln ( 9 x )}{x} d x

Frequently Asked Questions (FAQ)

What is the derivative of y=(3+5x-8sqrt(x))/x ?
The derivative of y=(3+5x-8sqrt(x))/x is (4sqrt(x)-3)/(x^2)
What is the first derivative of y=(3+5x-8sqrt(x))/x ?
The first derivative of y=(3+5x-8sqrt(x))/x is (4sqrt(x)-3)/(x^2)