What is (\partial)/(\partial x)(sin(ye^{10x})) ?

The answer to (\partial)/(\partial x)(sin(ye^{10x})) is cos(ye^{10x})ye^{10x}*10

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(\partial)/(\partial x)(sin(ye^{10x}))

\frac{\partial}{\partial x} (sin (y e^{10 x}))

cos (y e^{10 x}) y e^{10 x} \cdot 10

Solution steps

\frac{\partial}{\partial x} (sin (y e^{10 x}))

Treat

y

as a constant

Apply the chain rule:

cos (y e^{10 x}) \frac{\partial}{\partial x} (y e^{10 x})

= cos (y e^{10 x}) \frac{\partial}{\partial x} (y e^{10 x})

\frac{\partial}{\partial x} (y e^{10 x}) = y e^{10 x} \cdot 10

= cos (y e^{10 x}) y e^{10 x} \cdot 10

x \to - 2 lim (12 x + 11)

\frac{12}{x}

(- 3 x^{2} - 2)^{4}

\frac{x - cos ( x )}{x ^{2} + cot ( x )}

\int \frac{2 x ^{2} + 3 x + 6}{x ^{3} + 4 x} d x

What is (\partial)/(\partial x)(sin(ye^{10x})) ?
The answer to (\partial)/(\partial x)(sin(ye^{10x})) is cos(ye^{10x})ye^{10x}*10