What is (\partial)/(\partial x)(e^{3x^2}+4xy+5y^2) ?

The answer to (\partial)/(\partial x)(e^{3x^2}+4xy+5y^2) is 6e^{3x^2}x+4y

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(\partial)/(\partial x)(e^{3x^2}+4xy+5y^2)

\frac{\partial}{\partial x} (e^{3 x^{2}} + 4 x y + 5 y^{2})

6 e^{3 x^{2}} x + 4 y

Solution steps

\frac{\partial}{\partial x} (e^{3 x^{2}} + 4 x y + 5 y^{2})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (e^{3 x^{2}}) + \frac{\partial}{\partial x} (4 x y) + \frac{\partial}{\partial x} (5 y^{2})

\frac{\partial}{\partial x} (e^{3 x^{2}}) = e^{3 x^{2}} \cdot 6 x

\frac{\partial}{\partial x} (4 x y) = 4 y

\frac{\partial}{\partial x} (5 y^{2}) = 0

= e^{3 x^{2}} \cdot 6 x + 4 y + 0

Simplify

= 6 e^{3 x^{2}} x + 4 y

f (t) = t e^{t}

f (x) = cos (\frac{π x}{2}), at x = 0.7

x y d x - (x^{2} - x) d y = 0

\frac{\partial}{\partial x} (sin (x y) + cos (x y))

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What is (\partial)/(\partial x)(e^{3x^2}+4xy+5y^2) ?
The answer to (\partial)/(\partial x)(e^{3x^2}+4xy+5y^2) is 6e^{3x^2}x+4y