Question #9409e

2 Answers
Jan 9, 2018

4secxtanx+2cscxcotx

Explanation:

"differentiate using "color(blue)"standard derivatives"

•color(white)(x)d/dx(secx)=secxtanx

•color(white)(x)d/dx(cscx)=-cscxcotx

rArrd/dx(4secx-2cscx)

=4secxtanx-2(-cscxcotx)

=4secxtanx+2cscxcotx

Jan 9, 2018

d/dx(4sec(x)-2csc(x))=4sec(x)tan(x)+2csc(x)cot(x)

Explanation:

We have your original question

d/dx(4sec(x)-2csc(x))

Thankfully, this question isn't too bad, since the only operation between the x values is subtraction. All we really need to know for this question is

d/dx(sec(x))=sec(x)tan(x)

and

d/dx(csc(x))=-csc(x)cot(x)

So we can simplify your original question to

d/dx4sec(x)- d/dx2csc(x)

Since there are constants, we can take those out.

4d/dxsec(x)- 2d/dxcsc(x)

Finally, we can substitute what we found earlier to get the following:

4sec(x)tan(x)-2(-csc(x)cot(x))

And since there's a -2 being multiplied to -csc(x), the subtractions cancel out to get your final answer.

4sec(x)tan(x)+2csc(x)cot(x)