What is the derivative of x/(3-{z(x)}) ?

The derivative of x/(3-{z(x)}) is (3-{z}(x)+x derivative of {z}(x))/((3-{z)(x))^2}

What is the first derivative of x/(3-{z(x)}) ?

The first derivative of x/(3-{z(x)}) is (3-{z}(x)+x derivative of {z}(x))/((3-{z)(x))^2}

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\frac{d}{d x} (\frac{x}{3 - z ( x )})

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

Solution steps

\frac{d}{d x} (\frac{x}{3 - z ( x )})

Apply the Quotient Rule:

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

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

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

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

= \frac{1 \cdot ( 3 - z ( x ) ) - ( - \frac{d}{d x} ( z ( x ) ) ) x}{( 3 - z ( x ) ) ^{2}}

Simplify

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

(3) (7.8)

x \to - \infty lim (2 x)

\int - \frac{k}{x} d x

\int_{1}^{2} (5 x^{4} + 5) d x

\frac{d ^{2}}{d x ^{2}} ((5 x^{2} - 4 x) cos (x))

What is the derivative of x/(3-{z(x)}) ?
The derivative of x/(3-{z(x)}) is (3-{z}(x)+x derivative of {z}(x))/((3-{z)(x))^2}
What is the first derivative of x/(3-{z(x)}) ?
The first derivative of x/(3-{z(x)}) is (3-{z}(x)+x derivative of {z}(x))/((3-{z)(x))^2}