How do do you differentiate #f(x)= (x+sinx)/(cosx)#?
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(x) = \frac{x + \sin(x)}{\cos(x)} ):

Apply the quotient rule, which states that if ( f(x) = \frac{u(x)}{v(x)} ), then ( f'(x) = \frac{u'(x)v(x)  u(x)v'(x)}{[v(x)]^2} ).

Identify ( u(x) = x + \sin(x) ) and ( v(x) = \cos(x) ).

Find the derivatives ( u'(x) ) and ( v'(x) ).
 ( u'(x) = 1 + \cos(x) )
 ( v'(x) = \sin(x) )

Substitute the derivatives and the original functions into the quotient rule formula.
 ( f'(x) = \frac{(1 + \cos(x))\cos(x)  (x + \sin(x))(\sin(x))}{[\cos(x)]^2} )

Simplify the expression if necessary.
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7