What is (\partial)/(\partial x)(x^2yz^3(x-10y)) ?

The answer to (\partial)/(\partial x)(x^2yz^3(x-10y)) is yz^3(3x^2-20xy)

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(\partial)/(\partial x)(x^2yz^3(x-10y))

\frac{\partial}{\partial x} (x^{2} y z^{3} (x - 10 y))

y z^{3} (3 x^{2} - 20 x y)

Solution steps

\frac{\partial}{\partial x} (x^{2} y z^{3} (x - 10 y))

Treat

y, z

as constants

Take the constant out:

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

= y z^{3} \frac{\partial}{\partial x} (x^{2} (x - 10 y))

Apply the Product Rule:

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

f = x^{2}, g = x - 10 y

= y z^{3} (\frac{\partial}{\partial x} (x^{2}) (x - 10 y) + \frac{\partial}{\partial x} (x - 10 y) x^{2})

\frac{\partial}{\partial x} (x^{2}) = 2 x

\frac{\partial}{\partial x} (x - 10 y) = 1

= y z^{3} (2 x (x - 10 y) + 1 \cdot x^{2})

Simplify

y z^{3} (2 x (x - 10 y) + 1 \cdot x^{2}) : y z^{3} (3 x^{2} - 20 x y)

= y z^{3} (3 x^{2} - 20 x y)

\int arcsec (4 x) d x

(e^{t} x + 1) d x

\frac{\partial}{\partial x} (2 y + x)

\int y - y d y

\frac{13}{ln ( x )}

What is (\partial)/(\partial x)(x^2yz^3(x-10y)) ?
The answer to (\partial)/(\partial x)(x^2yz^3(x-10y)) is yz^3(3x^2-20xy)