What is the derivative of (15/x+(225)/(15-x)) ?

The derivative of (15/x+(225)/(15-x)) is (210x^2+450x-3375)/(x^2(-x+15)^2)

What is the first derivative of (15/x+(225)/(15-x)) ?

The first derivative of (15/x+(225)/(15-x)) is (210x^2+450x-3375)/(x^2(-x+15)^2)

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\frac{d}{d x} (\frac{15}{x} + \frac{225}{15 - x})

\frac{210 x ^{2} + 450 x - 3375}{x ^{2} ( - x + 15 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{15}{x} + \frac{225}{15 - x})

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (\frac{15}{x}) + \frac{d}{d x} (\frac{225}{15 - x})

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

\frac{d}{d x} (\frac{225}{15 - x}) = \frac{225}{( 15 - x ) ^{2}}

= - \frac{15}{x ^{2}} + \frac{225}{( 15 - x ) ^{2}}

Simplify

- \frac{15}{x ^{2}} + \frac{225}{( 15 - x ) ^{2}} : \frac{210 x ^{2} + 450 x - 3375}{x ^{2} ( - x + 15 ) ^{2}}

= \frac{210 x ^{2} + 450 x - 3375}{x ^{2} ( - x + 15 ) ^{2}}

x y y^{^{'}} = x^{6} + 3 y^{2}, y (e) = - e^{3}

\frac{d}{d x} ((3 x^{3} + 4) (x^{4} - 2 x))

x \to 0 lim (\frac{x ^{2} ln ( x )}{x})

\frac{\partial}{\partial x} ((y - 2) (arctan (x)))

\frac{d}{d x} (\frac{csc ( x )}{2 ^{x}})

What is the derivative of (15/x+(225)/(15-x)) ?
The derivative of (15/x+(225)/(15-x)) is (210x^2+450x-3375)/(x^2(-x+15)^2)
What is the first derivative of (15/x+(225)/(15-x)) ?
The first derivative of (15/x+(225)/(15-x)) is (210x^2+450x-3375)/(x^2(-x+15)^2)