What is the -derivative of 4e^x ?

The -derivative of 4e^x is -x derivative of 4e^x+4e^xx-4e^x+C

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Find the Derivative - d/dx 4e^x

\int - \frac{d}{d x} (4 e^{x}) d x

- x \frac{d}{d x} (4 e^{x}) + 4 e^{x} x - 4 e^{x} + C

Solution steps

\int - \frac{d}{d x} (4 e^{x}) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - \int \frac{d}{d x} (4 e^{x}) d x

Apply Integration By Parts

: \frac{d}{d x} (4 e^{x}) x - \int 4 e^{x} x d x

= - (\frac{d}{d x} (4 e^{x}) x - \int 4 e^{x} x d x)

\int 4 e^{x} x d x = 4 (e^{x} x - e^{x})

= - (\frac{d}{d x} (4 e^{x}) x - 4 (e^{x} x - e^{x}))

Simplify

- (\frac{d}{d x} (4 e^{x}) x - 4 (e^{x} x - e^{x})) : - x \frac{d}{d x} (4 e^{x}) + 4 e^{x} x - 4 e^{x}

= - x \frac{d}{d x} (4 e^{x}) + 4 e^{x} x - 4 e^{x}

Add a constant to the solution

= - x \frac{d}{d x} (4 e^{x}) + 4 e^{x} x - 4 e^{x} + C

- \frac{d}{d} y \frac{y}{x}

- \frac{d}{d x} y = sec (2 x)

\int (e^{a x}) d x

(4, 6), (- 4, - 6)

- \frac{d}{d} u arcsin (u)

What is the -derivative of 4e^x ?
The -derivative of 4e^x is -x derivative of 4e^x+4e^xx-4e^x+C