What is the derivative of (25/x+(100)/(15-x)) ?

The derivative of (25/x+(100)/(15-x)) is (75x^2+750x-5625)/(x^2(-x+15)^2)

What is the first derivative of (25/x+(100)/(15-x)) ?

The first derivative of (25/x+(100)/(15-x)) is (75x^2+750x-5625)/(x^2(-x+15)^2)

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\frac{d}{d x} (\frac{25}{x} + \frac{100}{15 - x})

\frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{25}{x} + \frac{100}{15 - x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{25}{x}) + \frac{d}{d x} (\frac{100}{15 - x})

\frac{d}{d x} (\frac{25}{x}) = - \frac{25}{x ^{2}}

\frac{d}{d x} (\frac{100}{15 - x}) = \frac{100}{( 15 - x ) ^{2}}

= - \frac{25}{x ^{2}} + \frac{100}{( 15 - x ) ^{2}}

Simplify

- \frac{25}{x ^{2}} + \frac{100}{( 15 - x ) ^{2}} : \frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}

= \frac{75 x ^{2} + 750 x - 5625}{x ^{2} ( - x + 15 ) ^{2}}

x^{3} - 4 x

\int x (a - x)^{\frac{5}{2}} d x

\int \frac{2}{x ^{10}} d x

\frac{d}{d x} (ln (14) \cdot 4 9^{x} \cdot 2^{2 x + 1})

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

What is the derivative of (25/x+(100)/(15-x)) ?
The derivative of (25/x+(100)/(15-x)) is (75x^2+750x-5625)/(x^2(-x+15)^2)
What is the first derivative of (25/x+(100)/(15-x)) ?
The first derivative of (25/x+(100)/(15-x)) is (75x^2+750x-5625)/(x^2(-x+15)^2)