How would you differentiate -3cosy times x squared?

Answer 1

((-3)cos(y))(x2)

Well first of all you need decide what rule you should use. Now, because they're multiplied together I'm going to use the product rule which is -

(dy/dx)= f'g +fg'

remember to write everything out -

f=((-3)cos(y))

f'=((3)sin(y))

g=x2

g'=2x

so from here it's pretty simple, you just sub in the values you have for each letter, remember to use brackets!

so....(dy/dx)= ((3)sin(y))(x2)+((-3cos(y))(2x)

Now you just need to simplify and gather like terms -

(dy/dx)=3x2siny-6xcosy

=3x(xsiny-cosy)

And there you have it!

Remember to check this yourself cause its been a while since I've studied this so I might have made a silly mistake somewhere. ^_^ Hope this helps!