What is (\partial)/(\partial x)(10(11x-3y+12)^5) ?

The answer to (\partial)/(\partial x)(10(11x-3y+12)^5) is 550(11x-3y+12)^4

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(\partial)/(\partial x)(10(11x-3y+12)^5)

\frac{\partial}{\partial x} (10 (11 x - 3 y + 12)^{5})

550 (11 x - 3 y + 12)^{4}

Solution steps

\frac{\partial}{\partial x} (10 (11 x - 3 y + 12)^{5})

Treat

y

as a constant

Take the constant out:

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

= 10 \frac{\partial}{\partial x} ((11 x - 3 y + 12)^{5})

Apply the chain rule:

5 (11 x - 3 y + 12)^{4} \frac{\partial}{\partial x} (11 x - 3 y + 12)

= 5 (11 x - 3 y + 12)^{4} \frac{\partial}{\partial x} (11 x - 3 y + 12)

\frac{\partial}{\partial x} (11 x - 3 y + 12) = 11

= 10 \cdot 5 (11 x - 3 y + 12)^{4} \cdot 11

Simplify

= 550 (11 x - 3 y + 12)^{4}

\frac{d}{d x} (x - \frac{3}{2})

\int csc^{2} (y) \frac{1}{1 + cot ( y )} d y

\frac{d}{d x} (\frac{x ^{2}}{y ^{3}})

x \to 2 lim (x^{2} + x + 2)

x \to 1 lim (sin (x))

What is (\partial)/(\partial x)(10(11x-3y+12)^5) ?
The answer to (\partial)/(\partial x)(10(11x-3y+12)^5) is 550(11x-3y+12)^4