What is (\partial)/(\partial x)(6xsin(x+2y-z)) ?

The answer to (\partial)/(\partial x)(6xsin(x+2y-z)) is 6(sin(x+2y-z)+xcos(x+2y-z))

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(\partial)/(\partial x)(6xsin(x+2y-z))

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

6 (sin (x + 2 y - z) + x cos (x + 2 y - z))

Solution steps

\frac{\partial}{\partial x} (6 x sin (x + 2 y - z))

Treat

y, z

as constants

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (x sin (x + 2 y - z))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = sin (x + 2 y - z)

= 6 (\frac{\partial}{\partial x} (x) sin (x + 2 y - z) + \frac{\partial}{\partial x} (sin (x + 2 y - z)) x)

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

\frac{\partial}{\partial x} (sin (x + 2 y - z)) = cos (x + 2 y - z)

= 6 (1 \cdot sin (x + 2 y - z) + cos (x + 2 y - z) x)

Simplify

= 6 (sin (x + 2 y - z) + x cos (x + 2 y - z))

\frac{\partial}{\partial y} (2 x^{2} + 2 y - 8)

\int (csc^{2} (x) + 4) d x

\frac{d}{d x} (x^{2} \cdot e^{2 x})

\int \frac{2 ^{2 x}}{1 + 2 ^{2 x}} d x

t \frac{d y}{d t} + 4 y = t^{2}

What is (\partial)/(\partial x)(6xsin(x+2y-z)) ?
The answer to (\partial)/(\partial x)(6xsin(x+2y-z)) is 6(sin(x+2y-z)+xcos(x+2y-z))