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

t an g e n t f (x) = 4 x^{2} - 2 x + 1

t an g e n t f (x) = 2 x + 1, at x = 3

s l o p e in t erce pt (- 1, - 1), (1, 5)

\frac{d}{d x} ((3 x - 1)^{4} (2 x + 1)^{- 3})

x y^{^{'}} - y = x^{2} + 5 x - 1

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