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Popular >

derivative of (x+4/(x-3))

Solution

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

Solution

- \frac{7}{( x - 3 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( x + 4 ) ( x - 3 ) - \frac{d}{d x} ( x - 3 ) ( x + 4 )}{( x - 3 ) ^{2}}

\frac{d}{d x} (x + 4) = 1

\frac{d}{d x} (x - 3) = 1

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

Simplify

\frac{1 \cdot ( x - 3 ) - 1 \cdot ( x + 4 )}{( x - 3 ) ^{2}} : - \frac{7}{( x - 3 ) ^{2}}

= - \frac{7}{( x - 3 ) ^{2}}

Popular Examples

derivative of cos^9(x)derivative of

cos^{9} (x)

limit as x approaches-5+of sqrt(25-x^2)

x \to - 5 + lim (25 - x^{2})

y^{''}+y=cos(3t),y(0)=1,y^'(0)=0

y^{^{''}} + y = cos (3 t), y (0) = 1, y^{^{'}} (0) = 0

derivative of f(x)=sqrt(8x)derivative of

f (x) = 8 x

slope of x^4-13x^2+36 slope

x^{4} - 13 x^{2} + 36

Frequently Asked Questions (FAQ)

What is the derivative of (x+4/(x-3)) ?
The derivative of (x+4/(x-3)) is -7/((x-3)^2)
What is the first derivative of (x+4/(x-3)) ?
The first derivative of (x+4/(x-3)) is -7/((x-3)^2)