What is the derivative of ((10-(2))/((x)))*((3+(1))/((x))) ?

The derivative of ((10-(2))/((x)))*((3+(1))/((x))) is -(64)/(x^3)

What is the first derivative of ((10-(2))/((x)))*((3+(1))/((x))) ?

The first derivative of ((10-(2))/((x)))*((3+(1))/((x))) is -(64)/(x^3)

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derivative of

(\frac{10 - ( 2 )}{( x )}) \cdot (\frac{3 + ( 1 )}{( x )})

- \frac{64}{x ^{3}}

Solution steps

\frac{d}{d x} (\frac{10 - 2}{x} \cdot \frac{3 + 1}{x})

Take the constant out:

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

= (10 - 2) (3 + 1) \frac{d}{d x} (\frac{1}{x} \cdot \frac{1}{x})

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = \frac{1}{x}, g = \frac{1}{x}

= (10 - 2) (3 + 1) (\frac{d}{d x} (\frac{1}{x}) \frac{1}{x} + \frac{d}{d x} (\frac{1}{x}) \frac{1}{x})

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

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

= (10 - 2) (3 + 1) ((- \frac{1}{x ^{2}}) \frac{1}{x} + (- \frac{1}{x ^{2}}) \frac{1}{x})

Simplify

(10 - 2) (3 + 1) ((- \frac{1}{x ^{2}}) \frac{1}{x} + (- \frac{1}{x ^{2}}) \frac{1}{x}) : - \frac{64}{x ^{3}}

= - \frac{64}{x ^{3}}

(\frac{1}{1 + e ^{x}})^{^{'}}

- 3 x x + 1

\int - 9 sec^{2} (x) d x

x \to π lim (\frac{e ^{3 x} - 1}{x})

\frac{\partial}{\partial x} (\frac{x}{x ^{2} + 16} \cdot y)

What is the derivative of ((10-(2))/((x)))*((3+(1))/((x))) ?
The derivative of ((10-(2))/((x)))*((3+(1))/((x))) is -(64)/(x^3)
What is the first derivative of ((10-(2))/((x)))*((3+(1))/((x))) ?
The first derivative of ((10-(2))/((x)))*((3+(1))/((x))) is -(64)/(x^3)