What is the derivative of e^{(x+y}-1) ?

The derivative of e^{(x+y}-1) is e^{x+y}((dy)/(dx)+1)

What is the first derivative of e^{(x+y}-1) ?

The first derivative of e^{(x+y}-1) is e^{x+y}((dy)/(dx)+1)

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\frac{d}{d x} (e^{(x + y)} - 1)

e^{x + y} (\frac{d y}{d x} + 1)

Solution steps

\frac{d}{d x} (e^{(x + y)} - 1)

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (e^{x + y}) - \frac{d}{d x} (1)

\frac{d}{d x} (e^{x + y}) = e^{x + y} (1 + \frac{d y}{d x})

\frac{d}{d x} (1) = 0

= e^{x + y} (1 + \frac{d y}{d x}) - 0

Simplify

= e^{x + y} (\frac{d y}{d x} + 1)

f (x) = (1 + 5 x)^{9}, (0, 1)

e^{- x}, 1

\frac{\partial}{\partial x} ((cos (x))^{2})

- \frac{1}{( x - 6 ) ^{2}}

\int csc (4 x) d x

What is the derivative of e^{(x+y}-1) ?
The derivative of e^{(x+y}-1) is e^{x+y}((dy)/(dx)+1)
What is the first derivative of e^{(x+y}-1) ?
The first derivative of e^{(x+y}-1) is e^{x+y}((dy)/(dx)+1)