For this question, how is the answer 3?:
Determine the slope of the tangent to the curve y = (3x)(sinx) at the point with x-coordinate π/2.

Question

For this question, how is the answer 3?:
Determine the slope of the tangent to the curve y = (3x)(sinx) at the point with x-coordinate π/2.

anonymous · Answer

i think i got it

anonymous · Answer

i found the derivative to be 3cosx^2 + 3sin x and subbed in π/2. then i got 3.079 as my answer

anonymous · Answer

pi/2

displayerror · Answer

How'd you get 3cosx^2? The answer should come out to be exactly 3.
$$f(x) = 3x$$
$$f'(x) = 3$$
$$g(x) = \sin{x}$$
$$g'(x) = \cos{x}$$

anonymous · Answer

i got that too. then i did this:
y'=(3x)(cosx)+(3)(sinx)
y'=3cosx^2 + 3sinx

displayerror · Answer

You can't multiply the $x$ in $3x$ with the $x$ in $\cos{x}$. It's two separate functions, $3x$ and $\cos{x}$.

anonymous · Answer

ohh but when I don't, I get 4.79 as my answer

displayerror · Answer

The derivative should be 
$$f'(x) = 3 \sin{x} + 3x\cos{x}$$
Evaluate with x = pi/2:
$$f'(\frac{\pi}{2}) = 3 \sin{\frac{\pi}{2}} + \frac{3\pi}{2}\cos{\frac{\pi}{2}}$$
What does $\sin{(\pi/2})$ equal?
What does $\cos{(\pi/2})$ equal?

anonymous · Answer

sin(pi/2) = 0.02741
cos(pi/2) = 0.9996

displayerror · Answer

Your calculator is in degree mode. Change it to radian mode and re-evaluate.

anonymous · Answer

Oh! now I'm getting 3!

anonymous · Answer

thanks a lot!