What is the derivative of 5x-tan(5x) ?

The derivative of 5x-tan(5x) is -5tan^2(5x)

What is the first derivative of 5x-tan(5x) ?

The first derivative of 5x-tan(5x) is -5tan^2(5x)

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\frac{d}{d x} (5 x - tan (5 x))

- 5 tan^{2} (5 x)

Solution steps

\frac{d}{d x} (5 x - tan (5 x))

Apply the Sum/Difference Rule:

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

= \frac{d}{d x} (5 x) - \frac{d}{d x} (tan (5 x))

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

\frac{d}{d x} (tan (5 x)) = sec^{2} (5 x) \cdot 5

= 5 - sec^{2} (5 x) \cdot 5

Simplify

5 - sec^{2} (5 x) \cdot 5 : - 5 tan^{2} (5 x)

= - 5 tan^{2} (5 x)

y^{^{'}} + y = 5 sin (2 t)

\frac{d ^{2}}{d x ^{2}} (\frac{1}{x ^{3}})

\int \frac{8}{x} d x

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

\frac{1}{10 x ^{\frac{9}{10}}}

What is the derivative of 5x-tan(5x) ?
The derivative of 5x-tan(5x) is -5tan^2(5x)
What is the first derivative of 5x-tan(5x) ?
The first derivative of 5x-tan(5x) is -5tan^2(5x)