What is (\partial)/(\partial y)((z)(3x+5y)^9) ?

The answer to (\partial)/(\partial y)((z)(3x+5y)^9) is 45z(3x+5y)^8

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(\partial)/(\partial y)((z)(3x+5y)^9)

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

45 z (3 x + 5 y)^{8}

Solution steps

\frac{\partial}{\partial y} ((z) (3 x + 5 y)^{9})

Treat

z, x

as constants

Take the constant out:

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

= z \frac{\partial}{\partial y} ((3 x + 5 y)^{9})

Apply the chain rule:

9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

= 9 (3 x + 5 y)^{8} \frac{\partial}{\partial y} (3 x + 5 y)

\frac{\partial}{\partial y} (3 x + 5 y) = 5

= z \cdot 9 (3 x + 5 y)^{8} \cdot 5

Simplify

= 45 z (3 x + 5 y)^{8}

\frac{36 - 57 x + 15 x ^{2} - x ^{3}}{x ( 6 - x ) ^{2}}

(x - 3 - 2 i) (x - 3 + 2 i)

, 900 q - 10 w - 10 q (45 - \frac{1}{2} q)

(x 3 + 2 x)^{2}

\frac{12 ( - 6 x ^{2} + 7 )}{( 6 x ^{2} + 7 ) ^{2}}

What is (\partial)/(\partial y)((z)(3x+5y)^9) ?
The answer to (\partial)/(\partial y)((z)(3x+5y)^9) is 45z(3x+5y)^8