Do you mean sin(x2) or sin(x)2?
In each case, you would apply the chain rule. The derivative of the sine function is the cosine, and the derivative with respect to x of axn is nax(n - 1).
So if you mean:
f(x) = sin(x2)
Then:
f'(x) = cos(x2) * 2x
If you mean:
f(x) = sin(x)2
Then:
f'(x) = 2sin(x) * cos(x)
6,561 (i solved it by using this sentence: (9x9) x (9x9)= 81x81=6,561
.5(x-sin(x)cos(x))+c
Cosine squared theta = 1 + Sine squared theta
No. Cos squared x is not the same as cos x squared. Cos squared x means cos (x) times cos (x) Cos x squared means cos (x squared)
cosx^2 differentiates too 2(cosx)^1 x the differential of cos which is -sin so u get -2sinxcosx use the chain rule!
6,561 (i solved it by using this sentence: (9x9) x (9x9)= 81x81=6,561
Answer 1 Put simply, sine squared is sinX x sinX. However, sine is a function, so the real question must be 'what is sinx squared' or 'what is sin squared x': 'Sin(x) squared' would be sin(x^2), i.e. the 'x' is squared before performing the function sin. 'Sin squared x' would be sin^2(x) i.e. sin squared times sin squared: sin(x) x sin(x). This can also be written as (sinx)^2 but means exactly the same. Answer 2 Sine squared is sin^2(x). If the power was placed like this sin(x)^2, then the X is what is being squared. If it's sin^2(x) it's telling you they want sin(x) times sin(x).
.5(x-sin(x)cos(x))+c
The deriviative of sin2 x + cos2 x is 2 cos x - 2 sin x
Cosine squared theta = 1 + Sine squared theta
If you mean x squared + 9, you differentiate this as follows: Use the differentiation formula for a power, to differentiate the x squared. Separately, use the differentiation formula for a constant, to differentiate the 9. Finally, use the differentiation formula for a sum to add up the parts.
No, they do not.
(1 - cos(2x))/2, where x is the variable. And/Or, 1 - cos(x)^2, where x is the variable.
Your question is insufficiently precise, but I'll try to answer anyway. "Sine squared theta" usually means "the value of the sine of theta, quantity squared". "Sine theta squared" usually means "the value of the sine of the quantity theta*theta". The two are not at all the same.
∫ cos(x)/sin2(x) dx = -cosec(x) + C C is the constant of integration.
∫ sin(x)/cos2(x) dx = sec(x) + C C is the constant of integration.
∫ 1/sin2(x) dx = -cot(x) + CC is the constant of integration.