What is (\partial)/(\partial x)(6e^{x^5y^3}) ?

The answer to (\partial)/(\partial x)(6e^{x^5y^3}) is 30e^{x^5y^3}x^4y^3

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(\partial)/(\partial x)(6e^{x^5y^3})

\frac{\partial}{\partial x} (6 e^{x^{5} y^{3}})

30 e^{x^{5} y^{3}} x^{4} y^{3}

Solution steps

\frac{\partial}{\partial x} (6 e^{x^{5} y^{3}})

Treat

y

as a constant

Take the constant out:

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

= 6 \frac{\partial}{\partial x} (e^{x^{5} y^{3}})

Apply the chain rule:

e^{x^{5} y^{3}} \frac{\partial}{\partial x} (x^{5} y^{3})

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

\frac{\partial}{\partial x} (x^{5} y^{3}) = 5 y^{3} x^{4}

= 6 e^{x^{5} y^{3}} \cdot 5 y^{3} x^{4}

Simplify

= 30 e^{x^{5} y^{3}} x^{4} y^{3}

\int 10 x^{3} y d y

y = \frac{( x )}{x ^{2} + 1}

5 x

f (x) = x^{4} - 17 x^{2} + 16

\int_{0}^{1} x^{2} - x^{3} d x

What is (\partial)/(\partial x)(6e^{x^5y^3}) ?
The answer to (\partial)/(\partial x)(6e^{x^5y^3}) is 30e^{x^5y^3}x^4y^3