What is the derivative of 1/(1+t) ?

The derivative of 1/(1+t) is -1/((1+t)^2)

What is the first derivative of 1/(1+t) ?

The first derivative of 1/(1+t) is -1/((1+t)^2)

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derivative of

\frac{1}{1 + t}

- \frac{1}{( 1 + t ) ^{2}}

Solution steps

\frac{d}{d t} (\frac{1}{1 + t})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= \frac{d}{d t} ((1 + t)^{- 1})

Apply the chain rule:

- \frac{1}{( 1 + t ) ^{2}} \frac{d}{d t} (1 + t)

= - \frac{1}{( 1 + t ) ^{2}} \frac{d}{d t} (1 + t)

\frac{d}{d t} (1 + t) = 1

= - \frac{1}{( 1 + t ) ^{2}} \cdot 1

Simplify

= - \frac{1}{( 1 + t ) ^{2}}

\frac{2 x}{x ^{4} + 1}

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

x \to 0 + lim ((1 + 4 x)^{\frac{5}{x}})

\frac{d y}{d x}, y^{5} = x^{7}

x^{2} + 3 x + \frac{1}{x ^{2}}

What is the derivative of 1/(1+t) ?
The derivative of 1/(1+t) is -1/((1+t)^2)
What is the first derivative of 1/(1+t) ?
The first derivative of 1/(1+t) is -1/((1+t)^2)