What is the derivative of 1-(a/x ^{b-1}) ?

The derivative of 1-(a/x ^{b-1}) is (a^{b-1}(b-1))/(x^b)

What is the first derivative of 1-(a/x ^{b-1}) ?

The first derivative of 1-(a/x ^{b-1}) is (a^{b-1}(b-1))/(x^b)

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

\frac{a ^{b - 1} ( b - 1 )}{x ^{b}}

Solution steps

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{a ^{b - 1} ( b - 1 )}{x ^{b}})

Simplify

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

x \to 0 lim (4 e^{x})

x^{11} arccot (x)

t \to (0) lim (ln (t))

y^{^{'}} = \frac{2 - 3 y}{200 + x}

y^{^{''}} + 2 y^{^{'}} = sin (t)

What is the derivative of 1-(a/x ^{b-1}) ?
The derivative of 1-(a/x ^{b-1}) is (a^{b-1}(b-1))/(x^b)
What is the first derivative of 1-(a/x ^{b-1}) ?
The first derivative of 1-(a/x ^{b-1}) is (a^{b-1}(b-1))/(x^b)