# How do you differentiate #f(x) = sqrt(sin^3(2-x^2) # using the chain rule?

Hence, by Chain Rule,

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

To differentiate ( f(x) = \sqrt{\sin^3(2-x^2)} ) using the chain rule:

- Identify the outer function ( g(x) = \sqrt{x} ) and the inner function ( h(x) = \sin^3(2-x^2) ).
- Differentiate the outer function with respect to its argument: ( g'(x) = \frac{1}{2\sqrt{x}} ).
- Differentiate the inner function with respect to ( x ): ( h'(x) = \frac{d}{dx}(\sin^3(2-x^2)) ).
- Apply the chain rule: ( \frac{d}{dx}(\sqrt{\sin^3(2-x^2)}) = g'(h(x)) \cdot h'(x) ).
- Substitute the derivatives: ( \frac{d}{dx}(\sqrt{\sin^3(2-x^2)}) = \frac{1}{2\sqrt{h(x)}} \cdot \frac{d}{dx}(\sin^3(2-x^2)) ).
- Compute ( h'(x) ) using the chain rule and derivative of ( \sin^3(2-x^2) ): ( h'(x) = -3\sin^2(2-x^2) \cdot \cos(2-x^2) \cdot (-2x) ).
- Simplify and combine terms to get the final result.

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

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.

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.

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.

- How do you find the derivative of #2cos^2(x)#?
- What is the slope of the tangent line of #(1-x)(4-y^2)-1/lny = C #, where C is an arbitrary constant, at #(1,2)#?
- How do you differentiate #x^2y^2+xy=2#?
- How do you differentiate #f(x)=(x^2+x)(e^x-2x)# using the product rule?
- (A) Sin(y/x) +ye^(2-x) = x-y (B) √y - 4ln x = cos (x+y) (C) e^(2y) + tan(1/x) =(x²/y) (D) ln y+2x =(3-y)^3 (E)xy²-sin(x+2y)=2x . Find the dy/dx (implicit differentiation)?

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