# What is the second derivative of #f(x)=cos(x^2) #?

We use chain rule here

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

Here,

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

To find the second derivative of ( f(x) = \cos(x^2) ), we first find the first derivative using the chain rule, and then differentiate again using the chain rule and product rule.

The first derivative is: [ f'(x) = -2x \sin(x^2) ]

To find the second derivative, we use the product rule and chain rule: [ f''(x) = \frac{d}{dx} (-2x) \sin(x^2) + (-2x) \frac{d}{dx} \sin(x^2) ]

Simplifying and applying the chain rule for the derivative of ( \sin(x^2) ): [ f''(x) = -2 \sin(x^2) - 4x^2 \cos(x^2) ]

So, the second derivative of ( f(x) = \cos(x^2) ) is ( f''(x) = -2 \sin(x^2) - 4x^2 \cos(x^2) ).

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

- What are the points of inflection, if any, of #f(x)=x^(1/3)*(x+3)^(2/3) #?
- For what values of x is #f(x)=(2x-1)(3x-5) (x-2)# concave or convex?
- What are the points of inflection of #f(x)=x^{2}e^{1 -x^2} #?
- How do you find intercepts, extrema, points of inflections, asymptotes and graph #f(x)=x/sqrt(x^2+7)#?
- What are the points of inflection of #f(x)=x^6 + 3x^5 - x^4 - 40x^3 - 60x^2 + 8x + 5 #?

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