# Differentiate #sinx# #/# #5x# + #sec^2 x"# ?

By signing up, you agree to our Terms of Service and Privacy Policy

To differentiate the function ( \frac{\sin(x)}{5x + \sec^2(x)} ), you can use the quotient rule of differentiation, which states that if you have a function ( \frac{f(x)}{g(x)} ), then its derivative is given by:

[ \frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) = \frac{f'(x)g(x) - f(x)g'(x)}{(g(x))^2} ]

So, applying the quotient rule to the given function:

[ \frac{d}{dx}\left(\frac{\sin(x)}{5x + \sec^2(x)}\right) = \frac{(5x + \sec^2(x))(\cos(x)) - \sin(x)(5 + 2\sec(x)\tan(x))}{(5x + \sec^2(x))^2} ]

This gives you the derivative of the given function.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided 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 one-sided 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 one-sided 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.

- How do you find the slope of the tangent line to the graph of the function #f(x)=3-2x# at (-1,5)?
- What is the equation of the normal line of #f(x)= -2x^2-10/x # at #x=2 #?
- How do you find the equation of the tangent line to the graph #f(x)=e^(1-x)# through point (1,1)?
- What are some applications in which you need to find the normal to the tangent line?
- How do you find the points where the graph of the function #y= 1/ (x^2)# has horizontal tangents?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7