Find equation of the tangent line to the curve x^2+ siny =xy^2 + 1 at (1,0)

Question

phi · Answer

can you find dy/dx ?  (using implicit differentiation)
or do you need help ?

sew01246 · Answer

i need help

phi · Answer

x^2+ siny =xy^2 + 1 

I assume you can find the derivative with respect to x of 
x^2 ?

phi · Answer

what is
$$ \frac{d}{dx} x^2 $$?

sew01246 · Answer

0?

phi · Answer

the derivative of a constant is 0

use the power rule

phi · Answer

the power rule is
$$ \frac{d}{dx} x^n = n x^{n-1} \frac{dx}{dx} = n x^{n-1}$$

sew01246 · Answer

so how would i put power rule to use?

phi · Answer

The very first derivatives you learn is the power rule.  The problem you posted is much more advanced, and requires implicit differentiation, product rule, and trig functions.

photon336 · Answer

Well, technically you also have to use product rule for differentiation too.  I agree with @phi for this problem there's alot going on here. 

if I were you I wouldn't attempt this until you understand the power rule first. 

first let's move the other term to the left hand side. 

$$x^{2}+siny-xy^{2} = 1 $$


then differentiate both sides 

$$\frac{ d }{ dx }(x+\sin(y)-xy^{2}) = \frac{ d }{ dx }(1)$$

phi · Answer

If you need more background or review, you can try Khan's videos https://www.khanacademy.org/math/calculus-home/differential-calculus/taking-derivatives

photon336 · Answer

But start off with the power rule, and the basic rules for differentiation first.

photon336 · Answer

otherwise it's not going to make sense.

sew01246 · Answer

okay, after I then differentiate both sides

sew01246 · Answer

what's next?

phi · Answer

Here is a graph of the problem

sew01246 · Answer

Thanks for the video, as you can see I'm struggling with this problem.

photon336 · Answer

what is 

$$\frac{ d }{ dx } (x^{2}) = ? $$

photon336 · Answer

@sew01246

sew01246 · Answer

0?

photon336 · Answer

Here is the rule $$\frac{ d }{ dx } x^{n} = nx^{n-1}$$

photon336 · Answer

in $$x^{2} \rightarrow what~is~n?$$

sew01246 · Answer

1?

photon336 · Answer

$$\frac{ d }{ dx } x^2 = 2x^{2-1} = 2x$$

photon336 · Answer

@sew01246  can you see why?

sew01246 · Answer

no, can you explain?

photon336 · Answer

x^2 what is the exponent ?