How do you take the derivative of # y=tan^2(x^3)#?
You'll get this
As a result, your target derivative will equal
By signing up, you agree to our Terms of Service and Privacy Policy
To take the derivative of (y = \tan^2(x^3)), you can use the chain rule and the derivative of the tangent function:

Apply the chain rule: [\frac{d}{dx} \tan^2(u) = 2\tan(u) \cdot \frac{d}{dx} \tan(u)]

Let (u = x^3), so (y = \tan^2(u)).

Find (\frac{d}{du} \tan(u)) and (\frac{d}{dx} x^3).
 (\frac{d}{du} \tan(u) = \sec^2(u) \cdot \frac{d}{du} u)
 (\frac{d}{dx} x^3 = 3x^2)

Substitute back: [\frac{d}{dx} \tan^2(x^3) = 2\tan(x^3) \cdot \sec^2(x^3) \cdot 3x^2]
So, the derivative of (y = \tan^2(x^3)) is: [y' = 6x^2 \tan(x^3) \sec^2(x^3)]
By signing up, you agree to our Terms of Service and Privacy Policy
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
When evaluating a onesided 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.
 98% accuracy study help
 Covers math, physics, chemistry, biology, and more
 Stepbystep, indepth guides
 Readily available 24/7