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

The answer to (\partial)/(\partial x)(3^{2x}+5^{4y}+2x+y^4) is 2ln(3)*9^x+2

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

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

2 ln (3) \cdot 9^{x} + 2

Solution steps

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

Simplify

3^{2 x} + 5^{4 y} + 2 x + y^{4} : 9^{x} + 62 5^{y} + 2 x + y^{4}

= \frac{\partial}{\partial x} (9^{x} + 62 5^{y} + 2 x + y^{4})

Treat

y

as a constant

Apply the Sum/Difference Rule:

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

= \frac{\partial}{\partial x} (9^{x}) + \frac{\partial}{\partial x} (62 5^{y}) + \frac{\partial}{\partial x} (2 x) + \frac{\partial}{\partial x} (y^{4})

\frac{\partial}{\partial x} (9^{x}) = 2 ln (3) \cdot 9^{x}

\frac{\partial}{\partial x} (62 5^{y}) = 0

\frac{\partial}{\partial x} (2 x) = 2

\frac{\partial}{\partial x} (y^{4}) = 0

= 2 ln (3) \cdot 9^{x} + 0 + 2 + 0

Simplify

= 2 ln (3) \cdot 9^{x} + 2

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

\int x 2 - \frac{1}{2 x} d x

x \to 0 lim (\frac{x + 6}{x ^{2} + 3})

\int x^{4} sec^{2} (x^{5} + 2) d x

y^{^{'}} + 3 y = 2 sin (e^{3 x})

What is (\partial)/(\partial x)(3^{2x}+5^{4y}+2x+y^4) ?
The answer to (\partial)/(\partial x)(3^{2x}+5^{4y}+2x+y^4) is 2ln(3)*9^x+2