What is (\partial)/(\partial x)((z)(3x^4-2y^3)^3) ?

The answer to (\partial)/(\partial x)((z)(3x^4-2y^3)^3) is 36zx^3(3x^4-2y^3)^2

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(\partial)/(\partial x)((z)(3x^4-2y^3)^3)

\frac{\partial}{\partial x} ((z) (3 x^{4} - 2 y^{3})^{3})

36 z x^{3} (3 x^{4} - 2 y^{3})^{2}

Solution steps

\frac{\partial}{\partial x} ((z) (3 x^{4} - 2 y^{3})^{3})

Treat

z, y

as constants

Take the constant out:

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

= z \frac{\partial}{\partial x} ((3 x^{4} - 2 y^{3})^{3})

Apply the chain rule:

3 (3 x^{4} - 2 y^{3})^{2} \frac{\partial}{\partial x} (3 x^{4} - 2 y^{3})

= 3 (3 x^{4} - 2 y^{3})^{2} \frac{\partial}{\partial x} (3 x^{4} - 2 y^{3})

\frac{\partial}{\partial x} (3 x^{4} - 2 y^{3}) = 12 x^{3}

= z \cdot 3 (3 x^{4} - 2 y^{3})^{2} \cdot 12 x^{3}

Simplify

= 36 z x^{3} (3 x^{4} - 2 y^{3})^{2}

(\frac{1}{2}, \frac{7}{2}) y (- \frac{8}{5}, - \frac{6}{5})

- \frac{( 4 - 3 π ) a ^{3}}{18}

(e^{10} - 1)^{2}

8 + (8 - cos (4 t)) U (t - 2 π)

\frac{lo g _{10} ( x )}{( 1 + lo g _{10} ( x ) ) ^{2}}

What is (\partial)/(\partial x)((z)(3x^4-2y^3)^3) ?
The answer to (\partial)/(\partial x)((z)(3x^4-2y^3)^3) is 36zx^3(3x^4-2y^3)^2