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Popular >

derivative of (x+7)/(sqrt(x))

Solution

derivative of

\frac{x + 7}{x}

Solution

\frac{x - 7}{2 x x}

Solution steps

\frac{d}{d x} (\frac{x + 7}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (x + 7) = 1

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

= \frac{1 \cdot x - \frac{1}{2 x} ( x + 7 )}{( x ) ^{2}}

Simplify

\frac{1 \cdot x - \frac{1}{2 x} ( x + 7 )}{( x ) ^{2}} : \frac{x - 7}{2 x x}

= \frac{x - 7}{2 x x}

Popular Examples

derivative of (cos(x)(cos(x)))

\frac{d}{d x} ((cos (x)) (cos (x)))

integral of 1/(xsqrt(a^2-x^2))

\int \frac{1}{x a ^{2} - x ^{2}} d x

(dy)/(dx)=(y-1)^2+0.01,y(0)=1

\frac{d y}{d x} = (y - 1)^{2} + 0.01, y (0) = 1

derivative of (e^x-1^2)

\frac{d}{d x} ((e^{x} - 1)^{2})

integral of ((x+3))/(x^2+11x+18)

\int \frac{( x + 3 )}{x ^{2} + 11 x + 18} d x

Frequently Asked Questions (FAQ)

What is the derivative of (x+7)/(sqrt(x)) ?
The derivative of (x+7)/(sqrt(x)) is (x-7)/(2xsqrt(x))
What is the first derivative of (x+7)/(sqrt(x)) ?
The first derivative of (x+7)/(sqrt(x)) is (x-7)/(2xsqrt(x))