What is (\partial)/(\partial x)(e^xtan(x-y)) ?

The answer to (\partial)/(\partial x)(e^xtan(x-y)) is e^xtan(x-y)+sec^2(x-y)e^x

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(\partial)/(\partial x)(e^xtan(x-y))

\frac{\partial}{\partial x} (e^{x} tan (x - y))

e^{x} tan (x - y) + sec^{2} (x - y) e^{x}

Solution steps

\frac{\partial}{\partial x} (e^{x} tan (x - y))

Treat

y

as a constant

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = e^{x}, g = tan (x - y)

= \frac{\partial}{\partial x} (e^{x}) tan (x - y) + \frac{\partial}{\partial x} (tan (x - y)) e^{x}

\frac{\partial}{\partial x} (e^{x}) = e^{x}

\frac{\partial}{\partial x} (tan (x - y)) = sec^{2} (x - y)

= e^{x} tan (x - y) + sec^{2} (x - y) e^{x}

\int \frac{cos ( x )}{6 - sin ( x )} d x

\int \frac{25 x ^{2}}{( x - 3 ) ( x + 2 ) ^{2}} d x

\int x arctan (x) d x

x \to 1 + lim (ln (ln (x)))

\frac{d}{d x} (e^{- 10 x})

What is (\partial)/(\partial x)(e^xtan(x-y)) ?
The answer to (\partial)/(\partial x)(e^xtan(x-y)) is e^xtan(x-y)+sec^2(x-y)e^x