What is the derivative of ({g}(x)/(h(x))) ?

The derivative of ({g}(x)/(h(x))) is (x derivative of {g}(x)-{g}(x))/(x^2h)

What is the first derivative of ({g}(x)/(h(x))) ?

The first derivative of ({g}(x)/(h(x))) is (x derivative of {g}(x)-{g}(x))/(x^2h)

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\frac{d}{d x} (\frac{g ( x )}{h ( x )})

\frac{x \frac{d}{d x} ( g ( x ) ) - g ( x )}{x ^{2} h}

Solution steps

\frac{d}{d x} (\frac{g ( x )}{h ( x )})

Treat

h

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{h} \frac{d}{d x} (\frac{g ( x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{h} \cdot \frac{\frac{d}{d x} ( g ( x ) ) x - \frac{d x}{d x} g ( x )}{x ^{2}}

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

= \frac{1}{h} \cdot \frac{\frac{d}{d x} ( g ( x ) ) x - 1 \cdot g ( x )}{x ^{2}}

Simplify

\frac{1}{h} \cdot \frac{\frac{d}{d x} ( g ( x ) ) x - 1 \cdot g ( x )}{x ^{2}} : \frac{x \frac{d}{d x} ( g ( x ) ) - g ( x )}{x ^{2} h}

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

f (x) = 4 x - 8

\int 9 x cos (3 x) d x

\int e^{- x} \cdot cos (2 x) d x

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

n = 1 \sum \infty \frac{n ^{4}}{n !}

What is the derivative of ({g}(x)/(h(x))) ?
The derivative of ({g}(x)/(h(x))) is (x derivative of {g}(x)-{g}(x))/(x^2h)
What is the first derivative of ({g}(x)/(h(x))) ?
The first derivative of ({g}(x)/(h(x))) is (x derivative of {g}(x)-{g}(x))/(x^2h)