# Thread: This is a pretty straight foward question (Trig.)

1. ## This is a pretty straight foward question (Trig.)

Find the gradient of the tangent to the curve y = x sin x^2 at the point where x = π/3

2. Hello,

Originally Posted by sweetG
Find the gradient of the tangent to the curve y = x sin x2 at the point where x = π/3
Let $f(x)=x \sin x^2$

The gradient of the tangent at the point where $x=\frac{\pi}{3}$ is $f'(\pi/3)$.

So first of all, calculate $f'(x)$ (applying product rule & chain rule) and then take $x=\frac{\pi}3$

3. Umm I'm really bad at differentiating trigonometric functions but could the answer possibly be: f '(x) = sinx^2 + 2x cos x^2

4. Originally Posted by sweetG
Umm I'm really bad at differentiating trigonometric functions but could the answer possibly be: f '(x) = sinx^2 + 2x cos x^2
Nearly !!

(uv)'=u'v+uv'
(x sin x²)'=(x)' sin x² + x (sin x²)'

you forgot this red x

5. f '(x) = sinx^2 + x(2x cos x^2)

Would that be the correct answer ?

And well if it is correct does that mean I just substitute x = π/3 into all the x's ?

Oh I'm so bad at this >_<

6. Originally Posted by sweetG
f '(x) = sinx^2 + x(2x cos x^2)

Would that be the correct answer ?

And well if it is correct does that mean I just substitute x = π/3 into all the x's ?

Oh I'm so bad at this >_<
yes, and yes !

You seem not to be bad since you know the basic rules This was just a careless mistake ^^ Am I wrong ?

7. Yup it was a careless mistake
but am this is the part that confuses me as well
coz am i supposed to substitute it into every x value there ?

f '(x) = sinx^2 + x(2x cos x^2)

so when x = π/3

Am I supposed to put x = π/3 in to all x's coz I dunno if its just me but that looks wrong ?! =S I'm so confused

Where do I sub in π/3 >_< sorry its pretty late here and I'm just not thinking properly at the moment

8. I'm just saying that well if I substituted π/3 in every single x I saw then that would be wrong, right ?

Argh I hate trigonometry >_<

9. Hi,

Given function is y=xsin(x^2)

to find the slope=m=y'=differentiate with respect to x by using product rule formula

y'=sinx^2+xcosx^2.2x

y'=sinx^2+2x^2cosx^2

gradient of the give curve at the point x=pi/3

y'=sin(pi/3)^2+2(pi/3)^3cos(pi/3)^2

here u can use calculator to get the answer .