Math, derivatives

Let g(x) = sin (cos x^3) Find g ' (x):

The choices are
a) -3x^2sinx^3cos(cos x^3)
b) -3x^2sinx^3sin(cos x^3)
c) -3x^2cosx^3sin(cos x^3)
d) 3x^2sin^2(cos x^3)

I'm not exactly sure where I should start.
Should I begin with d/dx of sin? Or do the inside derivative first...and do I have to separate cos and x^3 as well?

  1. 👍 0
  2. 👎 0
  3. 👁 116
  1. This is a multiple choice question and then the way you should attack the problem should be different than if you were asked to find the derivative of sin[cos(x^3)]

    What you do is you use the chain rule, accrding to which the derivative of
    sin(f(x)) = cos(f(x)) f'(x)

    Without calculkating anything, you immediately see that b) c) and d) cannot be right, so a) must be right.

    The prefactor -3x^2sin(x^3) is indeed the derivative of the argument of the sin. You only have to notice that it looks correct and then move on to the next question. In a test you can be given many multiple choice question and then the teacher will test if you can spot the correct answer within seconds.

    1. 👍 0
    2. 👎 0

Respond to this Question

First Name

Your Response

Similar Questions

  1. TRIG!

    Posted by hayden on Monday, February 23, 2009 at 4:05pm. sin^6 x + cos^6 x=1 - (3/4)sin^2 2x work on one side only! Responses Trig please help! - Reiny, Monday, February 23, 2009 at 4:27pm LS looks like the sum of cubes sin^6 x +

    asked by hayden on February 23, 2009
  2. Trigonometry

    Solve the equation for solutions in the interval 0

    asked by Renee on March 7, 2016
  3. tigonometry

    expres the following as sums and differences of sines or cosines cos8t * sin2t sin(a+b) = sin(a)cos(b) + cos(a)sin(b) replacing by by -b and using that cos(-b)= cos(b) sin(-b)= -sin(b) gives: sin(a-b) = sin(a)cos(b) - cos(a)sin(b)

    asked by Pablo on November 26, 2006
  4. algebra

    Can someone please help me do this problem? That would be great! Simplify the expression: sin theta + cos theta * cot theta I'll use A for theta. Cot A = sin A / cos A Therefore: sin A + (cos A * sin A / cos A) = sin A + sin A = 2

    asked by Valerie on February 18, 2007
  5. trig

    Reduce the following to the sine or cosine of one angle: (i) sin145*cos75 - cos145*sin75 (ii) cos35*cos15 - sin35*sin15 Use the formulae: sin(a+b)= sin(a) cos(b) + cos(a)sin(b) and cos(a+b)= cos(a)cos(b) - sin(a)sin)(b) (1)The

    asked by Paul C on November 26, 2006
  6. pre-cal

    Simplify the given expression........? (2sin2x)(cos6x) sin 2x and cos 6x can be expressed as a series of terms that involve sin x or cos x only, but the end result is not a simplification. sin 2x = 2 sinx cosx cos 6x = 32 cos^6 x

    asked by ethan on May 17, 2007
  7. Mathematics-Integration

    Question: Prove that [integrate {x*sin2x*sin[π/2*cos x]} dx] /(2x-π) } from (0-π) = [ integrate {sin x*cos x*sin[π/2*cos x} dx ] from (0-π). My thoughts on the question: We know that integrate f(x) dx from (0-a) = integrate

    asked by Shenaya on June 8, 2017
  8. Mathematics - Trigonometric Identities

    Let y represent theta Prove: 1 + 1/tan^2y = 1/sin^2y My Answer: LS: = 1 + 1/tan^2y = (sin^2y + cos^2y) + 1 /(sin^2y/cos^2y) = (sin^2y + cos^2y) + 1 x (cos^2y/sin^2y) = (sin^2y + cos^2y) + (sin^2y + cos^2y) (cos^2y/sin^2y) =

    asked by Anonymous on November 8, 2007
  9. math (trig)

    i have some problems doing trig the first one is: Show that cos(x/2) sin(3x/2) = ½(sinx + sin2x) i know that you are supposed to substitute all those trig function things in it but i kind of forgot how to the only that i can see

    asked by jacob on April 30, 2007
  10. Trig

    prove the identity (sinX)^6 +(cosX)^6= 1 - 3(sinX)^2 (cosX)^2 sinX^6= sinx^2 ^3 = (1-cosX^2)^3 = (1-2CosX^2 + cos^4) (1-cosX^2) then multiply that out 1-2CosX^2 + cos^4 - cosX^2 + 2cos^4 -cos^6 add that on the left to the cos^6,

    asked by JungJung on December 8, 2006

More Similar Questions