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Popular >

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

Solution

\frac{d}{d x} (\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

integral of 1/(sqrt(1-x^2)arcsin(x))

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

(\partial)/(\partial y)(x^2+yz)

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

derivative of ln(h+1/(2ax^2+b))

\frac{d}{d x} (ln (h + \frac{1}{2 a x ^{2}} + b))

limit as x approaches 0 of (1-cos(5x))/(sin(3x))

x \to 0 lim (\frac{1 - cos ( 5 x )}{sin ( 3 x )})

3(dr)/(ds)=e^{r-2s}

3 \frac{d r}{d s} = e^{r - 2 s}

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))