Question

How do you differentiate `f(x)=2sinx-tanx`?

Answer 1

The derivative is `2Cos(x)-(1/Cos^2(x))`- see below for how to do it.

Explanation:

If

`f(x)=2Sinx-Tan(x)`

For the sine part of the function, the derivative is simply: `2Cos(x)`

However, `Tan(x)` is a bit more tricky- you have to use the quotient rule.

Recall that `Tan(x)=(Sin(x)/Cos(x))`

Hence we can use The quotient rule

if`f(x)=(Sin(x)/Cos(x))`

Then

`f'(x)=((Cos^2(x)-(-Sin^2(x)))/(Cos^2(x)))`

`Sin^2(x)+Cos^2(x)=1`

`f'(x)=1/(Cos^2(x))`

So the complete function becomes
`f'(x)=2Cos(x)- (1/Cos^2(x))`

Or

`f'(x)=2Cos(x)-Sec^2(x)`

Answer 2

`f'(x)=2cosx-sec^2x`

Explanation:

`"utilising the "color(blue)"standard derivatives"`

`•color(white)(x)d/dx(sinx)=cosx" and "d/dx(tanx)=sec^2x`

`rArrf'(x)=2cosx-sec^2x`