## smileybug96 3 years ago how do i differentiate a function

1. tjones89

it depends on the function, there are different rules you can use for different types

2. cljohn

use the rules of differentiatin

3. smileybug96

what if i have like, sin(3x^3 +1) how would i do that?

4. cljohn

use the trig rules of differentiation, the derivative of sin is cos, the derivative of cosx is -sinx and the derivative of -sinx is -cosx. Last the derivative of -cosx is sinx, then the pattern starts over

5. cljohn

then you need to use the chain rule for 3x^3+1

6. smileybug96

so, im gonna say, cosx(9x+1)?

7. smileybug96

oh wait, imeant 9x^2 +1

8. cljohn

almost except you take the derivative of the outside function of sin(3x^3+1), disregard the 3x^3+1 and we will make that x, so the derivative of sinx is cos x.

9. smileybug96

10. cljohn

then replace the x and the derivative is cos(3x^3+1). BEcause there is a function within sinx we must use the chain rule. Now you need to to multiply by the derivative of the inside function of (3x^3+1) which is 9x. The derivative of the while funtion should now be 9xcos(3x^3+1)

11. smileybug96

ohhhh okay, thank you :)