Need Urgent Help with Derivatives? Get Expert Solutions Now!

  • Thread starter pyrosilver
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In summary, for the given functions, the derivatives would be 3sin^2(x^2 + sinx) * (2x + cosx), 31(cosx)^30 * (-sinx), and cos(x^3/(cosx^3)) * (3x^2(cosx^3) - 3sinx^2(cosx^2)).
  • #1
pyrosilver
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urgent -- need derivative help!

Homework Statement



f(x) = sin^3(x^2 + sinx)

f(x) = (cosx)^31^2

f(x) = sin(x^3/(cosx^3))

Homework Equations





The Attempt at a Solution



f(x) = sin^3(x^2 + sinx)
so i said it was 3sin(x^3+sinx) * (2x+cosx)

f(x) = (cosx)^31^2

i said this was the same as (cosx)^961, so 961(cosx)^960?

f(x) = sin(x^3/(cosx^3))
i said this was the same thing as sin(x^3cosx^-3), so cos(x^3cosx^-3) * (3x^2(cosx^-3) * (x^3(-3sinx^-4)?

please respond quickly, i have a fast deadline, gah thanks in advance
 
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  • #2


Hello there,

I understand that you are in need of help with derivatives. I will do my best to assist you with your questions.

For the first function, f(x) = sin^3(x^2 + sinx), you have the right idea. However, you have made a small mistake in your solution. The correct answer would be 3sin^2(x^2 + sinx) * (2x + cosx). The reason for this is because when you take the derivative of sin^3(x^2 + sinx), you need to use the chain rule. This means that you first take the derivative of the outer function, which is sin^3, and then multiply it by the derivative of the inner function, which is x^2 + sinx. So the correct solution would be 3sin^2(x^2 + sinx) * (2x + cosx).

For the second function, f(x) = (cosx)^31^2, you are on the right track. However, you have made a small mistake in your exponent. The correct answer would be 31(cosx)^30 * (-sinx). This is because when you have an exponent raised to another exponent, you need to use the power rule and multiply the exponents together. So the correct solution would be 31(cosx)^30 * (-sinx).

For the third function, f(x) = sin(x^3/(cosx^3)), you have made a small mistake in your solution. The correct answer would be cos(x^3/(cosx^3)) * (3x^2(cosx^3) - 3sinx^2(cosx^2)). This is because when you have a fraction in the argument of a function, you need to use the quotient rule. This means that you take the derivative of the numerator and multiply it by the denominator, then subtract the derivative of the denominator multiplied by the numerator, and finally divide it all by the denominator squared. So the correct solution would be cos(x^3/(cosx^3)) * (3x^2(cosx^3) - 3sinx^2(cosx^2)).

I hope this helps you with your derivatives. If you have any further questions, please don't hesitate to ask. Best of luck with your deadline!
 

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