Find the derivative. s=t^6tan(t)-sqrt t
confirm whether it is
s = (t^6)(tan(t)) - √t
or
s = t^(6tan(t)) - √t
Hi. I think Mr. Steve had already answered this before (on your previous post), you may want to check it out. I also answered this on that previous post too, but I'll just copy-paste my answer.
s = t^6 * tan(t) - sqrt(t)
ds/dt = t^6 (sec^2 (t)) + 6t^5 (tan(t)) - (1/2)(1/sqrt(t))
Just noticed that both Steve and Jai had already answered this question
http://www.jiskha.com/display.cgi?id=1381219879
Always check to see if your post has been answered before re-posting it again.
It would surely save some un-necessary duplication of work.
To find the derivative of the expression s = t^6tan(t) - √t, we can use the rules of differentiation.
1) We start by differentiating each term of the expression separately.
The derivative of t^6 is 6t^(6-1) = 6t^5.
To differentiate the term tan(t), we use the derivative of the tangent function, which is sec^2(t). Therefore, the derivative of tan(t) is sec^2(t).
The derivative of √t is (1/2)t^(-1/2) by the power rule.
2) Now, let's apply the sum and product rules to find the derivative of the expression.
The derivative of s with respect to t is given by:
ds/dt = (6t^5)(tan(t)) + t^6(sec^2(t)) - (1/2)t^(-1/2).
This can also be simplified as:
ds/dt = 6t^5tan(t) + t^6sec^2(t) - (1/2)t^(-1/2).
Thus, the derivative of the expression s = t^6tan(t) - √t is ds/dt = 6t^5tan(t) + t^6sec^2(t) - (1/2)t^(-1/2).