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Popular >

derivative of f(x)= x/(x-7)

Solution

derivative of

f (x) = \frac{x}{x - 7}

Solution

- \frac{7}{( x - 7 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

y^{''}+3y^'+2y= 1/(7+e^x)

y^{^{''}} + 3 y^{^{'}} + 2 y = \frac{1}{7 + e ^{x}}

derivative of 1+1/(2x)

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

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

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

x^{2} y^{^{'}} + x y = 6

derivative of (2x+1^2sqrt(3(2x+1)+10))

\frac{d}{d x} ((2 x + 1)^{2} 3 (2 x + 1) + 10)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)= x/(x-7) ?
The derivative of f(x)= x/(x-7) is -7/((x-7)^2)
What is the first derivative of f(x)= x/(x-7) ?
The first derivative of f(x)= x/(x-7) is -7/((x-7)^2)