What is the derivative of f(x)= 5/x ,\at P(4, 5/4) ?

The derivative of f(x)= 5/x ,\at P(4, 5/4) is -5/(x^2)

What is the first derivative of f(x)= 5/x ,\at P(4, 5/4) ?

The first derivative of f(x)= 5/x ,\at P(4, 5/4) is -5/(x^2)

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derivative of

f (x) = \frac{5}{x}, at P (4, \frac{5}{4})

- \frac{5}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{5}{x})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= 5 \frac{d}{d x} (x^{- 1})

Apply the Power Rule:

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

= 5 (- 1 \cdot x^{- 1 - 1})

Simplify

5 (- 1 \cdot x^{- 1 - 1}) : - \frac{5}{x ^{2}}

= - \frac{5}{x ^{2}}

y^{^{'}} = 8 x y - 2 x

\int - 15 x^{\frac{2}{3}} d x

\frac{d y}{d x} - y x = 0

x \to \infty lim (8 x^{3})

2 y^{^{''}} - 3 y^{^{'}} + y = e^{2 x} + sin (x)

What is the derivative of f(x)= 5/x ,\at P(4, 5/4) ?
The derivative of f(x)= 5/x ,\at P(4, 5/4) is -5/(x^2)
What is the first derivative of f(x)= 5/x ,\at P(4, 5/4) ?
The first derivative of f(x)= 5/x ,\at P(4, 5/4) is -5/(x^2)