What is the derivative of ax+bx+cx+2t(a+b+cz(x,t)) ?

The derivative of ax+bx+cx+2t(a+b+cz(x,t)) is a+b+c+2t(a+b+c) derivative of {z}(x,t)

What is the first derivative of ax+bx+cx+2t(a+b+cz(x,t)) ?

The first derivative of ax+bx+cx+2t(a+b+cz(x,t)) is a+b+c+2t(a+b+c) derivative of {z}(x,t)

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\frac{d}{d x} (a x + b x + c x + 2 t (a + b + c) z (x, t))

a + b + c + 2 t (a + b + c) \frac{d}{d x} (z (x, t))

Solution steps

\frac{d}{d x} (a x + b x + c x + 2 t (a + b + c) z (x, t))

Treat

a, b, c, t

as a constant

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (a x) + \frac{d}{d x} (b x) + \frac{d}{d x} (c x) + \frac{d}{d x} (2 t (a + b + c) z (x, t))

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

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

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

\frac{d}{d x} (2 t (a + b + c) z (x, t)) = 2 t (a + b + c) \frac{d}{d x} (z (x, t))

= a + b + c + 2 t (a + b + c) \frac{d}{d x} (z (x, t))

\frac{\partial}{\partial x} (a x + b y)

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

\int 3 x cos (x^{2}) d x

\int \frac{1}{t ^{2} - 2 t + 17} d t

\frac{\partial}{\partial x} (7 x y - 3 x^{2} y)

What is the derivative of ax+bx+cx+2t(a+b+cz(x,t)) ?
The derivative of ax+bx+cx+2t(a+b+cz(x,t)) is a+b+c+2t(a+b+c) derivative of {z}(x,t)
What is the first derivative of ax+bx+cx+2t(a+b+cz(x,t)) ?
The first derivative of ax+bx+cx+2t(a+b+cz(x,t)) is a+b+c+2t(a+b+c) derivative of {z}(x,t)