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

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

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(\partial)/(\partial r)((x)(r+3s-t))

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

x

Solution steps

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

Treat

x, s, t

as constants

Take the constant out:

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

= x \frac{\partial}{\partial r} (r + 3 s - t)

Apply the Sum/Difference Rule:

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

= x (\frac{\partial}{\partial r} (r) + \frac{\partial}{\partial r} (3 s) - \frac{\partial}{\partial r} (t))

\frac{\partial}{\partial r} (r) = 1

\frac{\partial}{\partial r} (3 s) = 0

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

= x (1 + 0 - 0)

Simplify

= x

1 + \frac{0.732 ( z + 0.1 )}{( z - 1 ) ( z - 0.9512 )}

(10 x y^{3} + 12 x^{3} + 6) d x + (15 x^{2} y - 5) y d y

\frac{4 s}{( x + 2 ) ( x - 1 )}

\frac{38 x y}{( x ^{2} + y ^{2} + 1 ) ^{2}}

e^{- 2 t} (- sin (4) 4) + cos (4 t) (e^{- 2 t} - 2 t)

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