What is (\partial)/(\partial x)(e^{7x^2+5y^2}) ?

The answer to (\partial)/(\partial x)(e^{7x^2+5y^2}) is e^{7x^2+5y^2}*14x

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(\partial)/(\partial x)(e^{7x^2+5y^2})

\frac{\partial}{\partial x} (e^{7 x^{2} + 5 y^{2}})

e^{7 x^{2} + 5 y^{2}} \cdot 14 x

Solution steps

\frac{\partial}{\partial x} (e^{7 x^{2} + 5 y^{2}})

Treat

y

as a constant

Apply the chain rule:

e^{7 x^{2} + 5 y^{2}} \frac{\partial}{\partial x} (7 x^{2} + 5 y^{2})

= e^{7 x^{2} + 5 y^{2}} \frac{\partial}{\partial x} (7 x^{2} + 5 y^{2})

\frac{\partial}{\partial x} (7 x^{2} + 5 y^{2}) = 14 x

= e^{7 x^{2} + 5 y^{2}} \cdot 14 x

\int 4 csc^{2} (x) d x

f (x) = 4 x^{2} - 2 x + 1

\int \frac{5 x ^{4}}{1 + x ^{5}} d x

f (x) = 2 x + 1, at x = 3

g (t) = tan (cos (2 t))

What is (\partial)/(\partial x)(e^{7x^2+5y^2}) ?
The answer to (\partial)/(\partial x)(e^{7x^2+5y^2}) is e^{7x^2+5y^2}*14x