# How do you find the derivative of #f(x)=sec(3x)csc(5x)#?

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

We need to use the product rule to differentiate this function:

For #f(x) = g(x)h(x), f'(x) = h(x)g'(x) + g(x)h'(x)

For the derivatives of the reciprocal trig functions, see https://tutor.hix.ai

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

To find the derivative of ( f(x) = \sec(3x) \csc(5x) ), you can use the product rule. The product rule states that if you have a function in the form ( f(x) = u(x) \cdot v(x) ), then the derivative is given by:

[ f'(x) = u'(x) \cdot v(x) + u(x) \cdot v'(x) ]

In this case, ( u(x) = \sec(3x) ) and ( v(x) = \csc(5x) ). We need to find ( u'(x) ) and ( v'(x) ) first.

[ u'(x) = 3\sec(3x)\tan(3x) ] [ v'(x) = -5\csc(5x)\cot(5x) ]

Now, apply the product rule:

[ f'(x) = 3\sec(3x)\tan(3x) \cdot \csc(5x) + \sec(3x) \cdot (-5\csc(5x)\cot(5x)) ]

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 derivative of # (e^(2x)) * (cos 2x)#?
- Why are the derivatives of periodic functions periodic?
- How do you differentiate #y=(1+sinx)/(x+cosx)#?
- If f(x)=lim of 1/(1+nsin^2pix) as n approaches to infinity,find the value of f(x) for all real values of x?
- Could you show me the workings of this polynomial function f(x)=cos x ?

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