B What's the derivative of sin^3(x+1) ^2?

[Odette]

Can someone explain it to me step by step?

 

[FactChecker]

Add parenthesis to show clearly what the equation is and what the exponents are applied to.

 

[Odette]

Can someone explain it to me step by step?

Add parenthesis to show clearly what the equation is and what the exponents are applied to.

 

[FactChecker]

You can apply the chain rule repeatedly to (sin((x+1)²))³ = f(g(h(x))), where f(g) = g³, g(h)=sin(h), and h(x)=(x+1)².

The overall equation is
df/dx = df/dg|_g ⋅ dg/dh|_h ⋅ dh/dx

df/dg = 3g²; dg/dh = cos(h); dh/dx = 2(x+1).

Substituting in gives df/dx = 3(sin((x+1)²))² ⋅ cos((x+1)²) ⋅ 2(x+1)

 

[Odette]

You can apply the chain rule repeatedly to (sin((x+1)²))³ = f(g(h(x))), where f(g) = g³, g(h)=sin(h), and h(x)=(x+1)².

The overall equation is
df/dx = df/dg|_g ⋅ dg/dh|_h ⋅ dh/dx

df/dg = 3g²; dg/dh = cos(h); dh/dx = 2(x+1).

Substituting in gives df/dx = 3(sin((x+1)²))² ⋅ cos((x+1)²) ⋅ 2(x+1)

Thank you!