What is the derivative of x(1-4/(x+3)) ?

The derivative of x(1-4/(x+3)) is -(12)/((x+3)^2)+1

What is the first derivative of x(1-4/(x+3)) ?

The first derivative of x(1-4/(x+3)) is -(12)/((x+3)^2)+1

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derivative of

x (1 - \frac{4}{x + 3})

- \frac{12}{( x + 3 ) ^{2}} + 1

Solution steps

\frac{d}{d x} (x (1 - \frac{4}{x + 3}))

Apply the Product Rule:

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

f = x, g = 1 - \frac{4}{x + 3}

= \frac{d x}{d x} (1 - \frac{4}{x + 3}) + \frac{d}{d x} (1 - \frac{4}{x + 3}) x

\frac{d x}{d x} = 1

\frac{d}{d x} (1 - \frac{4}{x + 3}) = \frac{4}{( x + 3 ) ^{2}}

= 1 \cdot (1 - \frac{4}{x + 3}) + \frac{4}{( x + 3 ) ^{2}} x

Simplify

1 \cdot (1 - \frac{4}{x + 3}) + \frac{4}{( x + 3 ) ^{2}} x : - \frac{12}{( x + 3 ) ^{2}} + 1

= - \frac{12}{( x + 3 ) ^{2}} + 1

\frac{d}{d x} (\frac{2}{e ^{\frac{x}{2}} + e ^{- \frac{x}{2}}})

f (x) = 5 tan (3 x)

n = 1 \sum \infty \frac{n - 5}{n + 2}

f (x) = \frac{1}{x ^{2}} - x

What is the derivative of x(1-4/(x+3)) ?
The derivative of x(1-4/(x+3)) is -(12)/((x+3)^2)+1
What is the first derivative of x(1-4/(x+3)) ?
The first derivative of x(1-4/(x+3)) is -(12)/((x+3)^2)+1