What is the derivative of f(x)=cos((x^2-25)/(x-5)) ?

The derivative of f(x)=cos((x^2-25)/(x-5)) is -sin(x+5)

What is the first derivative of f(x)=cos((x^2-25)/(x-5)) ?

The first derivative of f(x)=cos((x^2-25)/(x-5)) is -sin(x+5)

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derivative of

f (x) = cos (\frac{x ^{2} - 25}{x - 5})

- sin (x + 5)

Solution steps

\frac{d}{d x} (cos (\frac{x ^{2} - 25}{x - 5}))

Simplify

cos (\frac{x ^{2} - 25}{x - 5}) : cos (x + 5)

= \frac{d}{d x} (cos (x + 5))

Apply the chain rule:

- sin (x + 5) \frac{d}{d x} (x + 5)

= - sin (x + 5) \frac{d}{d x} (x + 5)

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

= - sin (x + 5) \cdot 1

Simplify

= - sin (x + 5)

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What is the derivative of f(x)=cos((x^2-25)/(x-5)) ?
The derivative of f(x)=cos((x^2-25)/(x-5)) is -sin(x+5)
What is the first derivative of f(x)=cos((x^2-25)/(x-5)) ?
The first derivative of f(x)=cos((x^2-25)/(x-5)) is -sin(x+5)