What is (\partial)/(\partial x)(-210(5x-y)^5) ?

The answer to (\partial)/(\partial x)(-210(5x-y)^5) is -5250(5x-y)^4

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(\partial)/(\partial x)(-210(5x-y)^5)

\frac{\partial}{\partial x} (- 210 (5 x - y)^{5})

- 5250 (5 x - y)^{4}

Solution steps

\frac{\partial}{\partial x} (- 210 (5 x - y)^{5})

Treat

y

as a constant

Take the constant out:

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

= - 210 \frac{\partial}{\partial x} ((5 x - y)^{5})

Apply the chain rule:

5 (5 x - y)^{4} \frac{\partial}{\partial x} (5 x - y)

= 5 (5 x - y)^{4} \frac{\partial}{\partial x} (5 x - y)

\frac{\partial}{\partial x} (5 x - y) = 5

= - 210 \cdot 5 (5 x - y)^{4} \cdot 5

Simplify

= - 5250 (5 x - y)^{4}

What is (\partial)/(\partial x)(-210(5x-y)^5) ?
The answer to (\partial)/(\partial x)(-210(5x-y)^5) is -5250(5x-y)^4