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)

Popular >

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}

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

\frac{x ^{3} + 6 x}{3}

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

\int \frac{x}{2 - x - x ^{2}} d x

x y^{2} \frac{d y}{d x} = y^{3} + x^{3}

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)