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Odette
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Member warned that HW posts must include some effort
Can someone explain it to me step by step?
What's the derivative of sin^3(x+1) ^2?
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In summary, the conversation discusses using the chain rule to find the derivative of a complex equation involving exponents and trigonometric functions. The overall equation for the chain rule is provided, along with the specific values for the derivatives of each part of the equation. Substituting in these values gives the final derivative.
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Add parenthesis to show clearly what the equation is and what the exponents are applied to.
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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)
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)
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Odette
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Thank you!FactChecker said:
1. What is the derivative of sin^3(x+1) ^2?
The derivative of sin^3(x+1) ^2 is 6sin^2(x+1)cos(x+1).
2. How do you find the derivative of sin^3(x+1) ^2?
To find the derivative of sin^3(x+1) ^2, you can use the chain rule and the power rule.
3. Can you simplify the derivative of sin^3(x+1) ^2?
Yes, the derivative can be simplified to 6sin^2(x+1)cos(x+1).
4. Is there a general formula for finding the derivative of power functions?
Yes, the general formula for finding the derivative of a power function is n* x^(n-1), where n is the power.
5. Why is the derivative of sin^3(x+1) ^2 not 3sin^2(x+1)cos(x+1)?
The derivative of sin^3(x+1) ^2 is not 3sin^2(x+1)cos(x+1) because of the chain rule. The function is raised to the power of 2, so the derivative must also take into account the power of 2.
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