What is (\partial)/(\partial x)(60e^{x^6y}x^5y) ?

The answer to (\partial)/(\partial x)(60e^{x^6y}x^5y) is 60y(6e^{x^6y}x^{10}y+5e^{x^6y}x^4)

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(\partial)/(\partial x)(60e^{x^6y}x^5y)

\frac{\partial}{\partial x} (60 e^{x^{6} y} x^{5} y)

60 y (6 e^{x^{6} y} x^{10} y + 5 e^{x^{6} y} x^{4})

Solution steps

\frac{\partial}{\partial x} (60 e^{x^{6} y} x^{5} y)

Treat

y

as a constant

Take the constant out:

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

= 60 y \frac{\partial}{\partial x} (e^{x^{6} y} x^{5})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x^{6} y}, g = x^{5}

= 60 y (\frac{\partial}{\partial x} (e^{x^{6} y}) x^{5} + \frac{\partial}{\partial x} (x^{5}) e^{x^{6} y})

\frac{\partial}{\partial x} (e^{x^{6} y}) = e^{x^{6} y} \cdot 6 y x^{5}

\frac{\partial}{\partial x} (x^{5}) = 5 x^{4}

= 60 y (e^{x^{6} y} \cdot 6 y x^{5} x^{5} + 5 x^{4} e^{x^{6} y})

e^{x^{6} y} \cdot 6 y x^{5} x^{5} = 6 e^{x^{6} y} x^{10} y

= 60 y (6 e^{x^{6} y} x^{10} y + 5 e^{x^{6} y} x^{4})

\int_{4}^{5} \frac{x}{x - 4} d x

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

\frac{1}{3 s + 5}

\frac{d}{d x} (\frac{x ^{2} + 3 x}{- 6})

\frac{d y}{d x} - 4 y = \frac{48 x}{y ^{2}}

What is (\partial)/(\partial x)(60e^{x^6y}x^5y) ?
The answer to (\partial)/(\partial x)(60e^{x^6y}x^5y) is 60y(6e^{x^6y}x^{10}y+5e^{x^6y}x^4)