What is the derivative of t/x ?

The derivative of t/x is -t/(x^2)

What is the first derivative of t/x ?

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

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\frac{d}{d x} (\frac{t}{x})

- \frac{t}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{t}{x})

Treat

t

as a constant

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= t (- 1 \cdot x^{- 1 - 1})

Simplify

t (- 1 \cdot x^{- 1 - 1}) : - \frac{t}{x ^{2}}

= - \frac{t}{x ^{2}}

y = (2 x - 5)^{\frac{1}{3}}

\int_{- 1}^{2} x d x

\frac{\partial}{\partial x} (\frac{1}{2} \cdot x \cdot y^{2})

x \to \infty lim (\frac{4}{x} - 2)

100 x^{2} + 400 x + 5000