How do you differentiate #f(x)= ( 4 secx )/ (x + 1) # using the quotient rule?
By signing up, you agree to our Terms of Service and Privacy Policy
To differentiate ( f(x) = \frac{4  \sec(x)}{x + 1} ) using the quotient rule:

Identify ( u(x) ) and ( v(x) ).
 Let ( u(x) = 4  \sec(x) ) and ( v(x) = x + 1 ).

Find ( u'(x) ) and ( v'(x) ).
 ( u'(x) = 0  \sec(x) \tan(x) )
 ( v'(x) = 1 )

Apply the quotient rule:
 ( f'(x) = \frac{v(x)u'(x)  u(x)v'(x)}{(v(x))^2} )
 Substitute the values: [ \begin{align*} f'(x) &= \frac{(x + 1)(0  \sec(x) \tan(x))  (4  \sec(x))(1)}{(x + 1)^2} \ &= \frac{x\sec(x)\tan(x)  \sec(x) + 1}{(x + 1)^2} \end{align*} ]
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.
 What is the derivative of # e^(x^2)#?
 How do you differentiate # f(x)=sqrt(ln(1/sqrt(xe^x))# using the chain rule.?
 How do you find the derivative of #1/x+1/y=7#?
 What is the slope of the tangent line of #(xy)e^(xy)= C #, where C is an arbitrary constant, at #(2,1)#?
 How do you differentiate #y=x^3/(1x^2)#?
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7