What is (\partial)/(\partial x)(6x^2e^y-7xy^3) ?

The answer to (\partial)/(\partial x)(6x^2e^y-7xy^3) is 12e^yx-7y^3

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(\partial)/(\partial x)(6x^2e^y-7xy^3)

\frac{\partial}{\partial x} (6 x^{2} e^{y} - 7 x y^{3})

12 e^{y} x - 7 y^{3}

Solution steps

\frac{\partial}{\partial x} (6 x^{2} e^{y} - 7 x y^{3})

Treat

y

as a constant

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{\partial}{\partial x} (6 x^{2} e^{y}) - \frac{\partial}{\partial x} (7 x y^{3})

\frac{\partial}{\partial x} (6 x^{2} e^{y}) = 12 e^{y} x

\frac{\partial}{\partial x} (7 x y^{3}) = 7 y^{3}

= 12 e^{y} x - 7 y^{3}

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

\int z e^{y} d y

\frac{d y}{d t} = 1 + t + y + t y

\frac{d}{d x} (x^{2} + 2 x - 8)

\frac{\partial}{\partial x} (e^{- x} tan (y))

What is (\partial)/(\partial x)(6x^2e^y-7xy^3) ?
The answer to (\partial)/(\partial x)(6x^2e^y-7xy^3) is 12e^yx-7y^3