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

The derivative of y(1+e^x) is (dy)/(dx)(1+e^x)+e^xy

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

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

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

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

Solution steps

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

Apply the Product Rule:

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

f = y, g = 1 + e^{x}

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

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

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

x \to 1 lim (0.9 9^{2 - 1})

\frac{d}{d x} (- \frac{13}{x ^{5}})

\frac{\partial}{\partial y} (- sin (x))

3 x arcsin (x)

\frac{d}{d x} (\frac{2 ( 3 x ^{4} - 5 )}{x ^{3}})

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