What is (\partial)/(\partial x)((z)(2x+3y)^{10}) ?

The answer to (\partial)/(\partial x)((z)(2x+3y)^{10}) is 20z(2x+3y)^9

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(\partial)/(\partial x)((z)(2x+3y)^{10})

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

20 z (2 x + 3 y)^{9}

Solution steps

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

Treat

z, y

as constants

Take the constant out:

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

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

Apply the chain rule:

10 (2 x + 3 y)^{9} \frac{\partial}{\partial x} (2 x + 3 y)

= 10 (2 x + 3 y)^{9} \frac{\partial}{\partial x} (2 x + 3 y)

\frac{\partial}{\partial x} (2 x + 3 y) = 2

= z \cdot 10 (2 x + 3 y)^{9} \cdot 2

Simplify

= 20 z (2 x + 3 y)^{9}

\frac{7}{( x - 1 ) ( x + 6 )}

\frac{x ^{3} - 4 x ^{2} + 2 x + 5}{x ( x + 3 ) ^{6} ( x - 2 ) ^{6} ( x ^{2} + 9 )}

(0, 3) y (0, - 3)

\frac{7 x + 9}{( x + 2 ) ( 3 x + 1 )}

e^{x} cos (x) (e^{x} sin (x) + cos (x) e^{x})

What is (\partial)/(\partial x)((z)(2x+3y)^{10}) ?
The answer to (\partial)/(\partial x)((z)(2x+3y)^{10}) is 20z(2x+3y)^9