What is the derivative of ((qx+r))/((sx+t)) ?

The derivative of ((qx+r))/((sx+t)) is x/(xs+t)

What is the first derivative of ((qx+r))/((sx+t)) ?

The first derivative of ((qx+r))/((sx+t)) is x/(xs+t)

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derivative of

\frac{( q x + r )}{( s x + t )}

\frac{x}{x s + t}

Solution steps

\frac{d}{d q} (\frac{q x + r}{s x + t})

Treat

x, r, s, t

as constants

Take the constant out:

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

= \frac{1}{s x + t} \frac{d}{d q} (q x + r)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{s x + t} (\frac{d}{d q} (q x) + \frac{d r}{d q})

\frac{d}{d q} (q x) = x

\frac{d r}{d q} = 0

= \frac{1}{s x + t} (x + 0)

Simplify

\frac{1}{s x + t} (x + 0) : \frac{x}{x s + t}

= \frac{x}{x s + t}

f (x) = \frac{e ^{x}}{3 x ^{2} + 2 x ^{4}}

\frac{d}{d x} (2 x (7 x^{2} - 2)^{4})

\int_{0}^{l n (5)} e^{x} (3 - 4 e^{x}) d x

y = e^{2}, x = 0, x = 3

\frac{d}{d x} (x e^{r (x) x})

What is the derivative of ((qx+r))/((sx+t)) ?
The derivative of ((qx+r))/((sx+t)) is x/(xs+t)
What is the first derivative of ((qx+r))/((sx+t)) ?
The first derivative of ((qx+r))/((sx+t)) is x/(xs+t)