How do you differentiate #g(θ) = cos(θ) - 4sin(θ)#?

Answer 1

#g'(theta)=-sintheta-4costheta#

The #color(blue)"trigonometric functions"# have standard derivatives.

#color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(cosx)=-sinx" and " d/dx(sinx)=cosx)color(white)(2/2)|)))#

#rArrg'(theta)=-sintheta-4costheta#

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

Answer 2

Samantha Adkison

To differentiate ( g(\theta) = \cos(\theta) - 4\sin(\theta) ):

[ \frac{d}{d\theta}[\cos(\theta)] = -\sin(\theta) ] [ \frac{d}{d\theta}[\sin(\theta)] = \cos(\theta) ]

Apply these derivatives to ( g(\theta) ):

[ \frac{d}{d\theta}[g(\theta)] = -\sin(\theta) - 4\cos(\theta) ]

So, the derivative is: [ g'(\theta) = -\sin(\theta) - 4\cos(\theta) ]

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

Answer from HIX Tutor

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.