Derivative of trigonometric functions

In summary, the product rule is used to find the derivative of the product of two functions, such as f(x) = sin4x and g(x) = cos3x. Using the chain rule, the derivative of f(x) is 4cos4x and the derivative of g(x) is -3sin3x. When using the product rule, the derivative of f(x)g(x) is found by multiplying the derivative of f(x) with g(x) and adding it to the derivative of g(x) multiplied by f(x). Therefore, the final answer is 4cos4x(cos3x) - 3sin4x(sin3x). This answer cannot be simplified further.
  • #1
fr33pl4gu3
82
0
y = sin( 4 x ) cos( 3 x )

f(x) = sin4x
g(x) = cos3x
f'(x) = cos4x
g'(x) = -sin3x

And by using the product rule, i'll get:

cos4x(cos3x) - sin4x(sin3x)

Is the answer correct or can be simplify again??
 
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  • #2
Check the f'(x) and g'(x). Are you missing something?
 
  • #3
sin4x can be written in this way (4(sin x)) or not?
 
Last edited:
  • #5
Is it

f'(x)=4cos(4x)

??
 
Last edited:
  • #6
Yes :smile:
And the other?
 
  • #7
so the answer would be

4cos4x(cos3x) -3 sin4x(sin3x)

Correct??
 
  • #8
Yes.
 
  • #9
can my last answer be simplify one more step?
 
  • #10
Not any that I can think of. It can be re-arranged. Do you have a target answer?
 
  • #11
fr33pl4gu3 said:
sin4x can be written in this way (4(sin x)) or not?
Try to draw the graphs for y= 4 sinx and y=sin4x for x= 0,30,45,60,90 degrees etc. and see for yourself.
 

1. What is the derivative of sine and cosine?

The derivative of sine is cosine, and the derivative of cosine is negative sine.

2. How do you find the derivative of tangent?

The derivative of tangent can be found by using the quotient rule, where the numerator is the derivative of sine and the denominator is the derivative of cosine.

3. Is the derivative of secant equal to the derivative of tangent?

No, the derivative of secant is equal to the product of tangent and secant, while the derivative of tangent is equal to the quotient of sine and cosine.

4. Can the chain rule be applied to the derivative of trigonometric functions?

Yes, the chain rule can be applied to the derivative of trigonometric functions by treating the inner function as the variable and the outer function as the function to be differentiated.

5. How do you find the derivative of inverse trigonometric functions?

The derivative of inverse trigonometric functions can be found using the inverse function theorem, which states that the derivative of the inverse function is equal to the reciprocal of the derivative of the original function at the corresponding input value.

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