how do u derive sin^3(x^2 + 5)??

Answer 1

I was always taught to start from the very outside on problems like these and work your way in.

I'll rewrite it to make it clearer:

(sin(x^2+5))^3

So we start with the power:

We get 3*(sin(x^2+5))^2.

Then onto the sine function:

We get cos(x^2+5)

Then onto the most inside function of x^2+5:

We get 2x

So we collect all the terms

3*(sin(x^2+5))^2 * cos(x^2+5) * 2x

And we simplify to get

6*sin^2(x^2+5)*cos(x^2+5)*x

Answer 2

???
I'm not sure I understand what you're asking. The verb 'derive' usually means to arrive at an answer (in mathematics, frequently a formula or expression) by the application of the principles of logic on the stated parameters of the problem. Or to 'derive' a proof.

OTOH, if you're asking how do you take the derivative of sin^3(x^2 + 5), then let f(x) = x^3,
g(x) = sin(x), and h(x) = (x² + 5) and write the function as
f(g(h(x))) and apply the chain rule three times to get
3sin²(x² + 5)*cos(x²+5)*2x. Then collect the terms and you have
6x*sin²(x² + 5)*cos(x² + 5)

Doug

Answer 3

First you should derive the internal function.the answer is: 3*Sin^2(x^2+5)*Cos(X^2+5)*2*x

Answer 4

Okay, No, People, 60% of English isn't Latin. Actually even if it were 60% French, which it's not, it still wouldn't be 60% Latin due to what.....The FRANKISH (Germanic language that mixed with Latin to make French) influence. Also we have influences from North Germanic, Celtic, Greek, and many others, although West Germanic is the true origin of the language. In fact there is a reason that English is not a Romance language, but rather a West Germanic one..... Okay, Now the major 5 are as follows: Spanish, Italian, Portuguese, French, and Romanian. Others include: Catalan, Ladino, Romansch, Galician, Lombard, Gallo, Norman, amongst so many more.

Answer 5

3*{sin^2(x^2 + 5)} * { cos (x^2 + 5) }2x
=6 x { sin(x^2 + 5) }^2 { cos (x^2 + 5) }

Answer 6

Buy a TI-89 and it will derive it for you.