What is (\partial)/(\partial x)((3x-t)/(4s+5t)) ?

The answer to (\partial)/(\partial x)((3x-t)/(4s+5t)) is 3/(4s+5t)

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(\partial)/(\partial x)((3x-t)/(4s+5t))

\frac{\partial}{\partial x} (\frac{3 x - t}{4 s + 5 t})

\frac{3}{4 s + 5 t}

Solution steps

\frac{\partial}{\partial x} (\frac{3 x - t}{4 s + 5 t})

Treat

t, s

as constants

Take the constant out:

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

= \frac{1}{4 s + 5 t} \frac{\partial}{\partial x} (3 x - t)

Apply the Sum/Difference Rule:

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

= \frac{1}{4 s + 5 t} (\frac{\partial}{\partial x} (3 x) - \frac{\partial}{\partial x} (t))

\frac{\partial}{\partial x} (3 x) = 3

\frac{\partial}{\partial x} (t) = 0

= \frac{1}{4 s + 5 t} (3 - 0)

Simplify

\frac{1}{4 s + 5 t} (3 - 0) : \frac{3}{4 s + 5 t}

= \frac{3}{4 s + 5 t}

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What is (\partial)/(\partial x)((3x-t)/(4s+5t)) ?
The answer to (\partial)/(\partial x)((3x-t)/(4s+5t)) is 3/(4s+5t)