Find the equation of the tangent line to the curve
y=6tan(x) at point (pi/4, 6)

Question

Find the equation of the tangent line to the curve 
y=6tan(x) at point (pi/4, 6)

anonymous · Answer

thanks @suvesh253 ! can u help me one more time with this one?!

calculusfunctions · Answer

I'm assuming you know calculus?

anonymous · Answer

yes!

calculusfunctions · Answer

OK, so then you know that you have to first find the derivative (slope function), correct?

calculusfunctions · Answer

In order to find the equation of the tangent line, we must first find the slope of the tangent line, correct?

calculusfunctions · Answer

That is incorrect because$$\frac{ d(\tan x) }{ dx }=\sec ^{2}x$$

calculusfunctions · Answer

Please try again.

calculusfunctions · Answer

If$$y =6\tan x$$then $$\frac{ dy }{ dx }=?$$

anonymous · Answer

no clue

calculusfunctions · Answer

Derivatives of primary trigonometric functions:
The derivative of sine is cosine.
The derivative of cosine is negative sine.
The derivative of tangent is secant squared.

Knowing this, to take the derivative of any primary trigonometric function:
i). take the derivative of the angle and multiply by the amplitude (the number in front of the trig function).
ii). multiply this by the derivative of the trig function and always keep the angle the same.


Now try again.

calculusfunctions · Answer

For example:$$y =3\sin (2x + 3)$$
$$\frac{ dy }{ dx }=3[\frac{ d(2x +3) }{ dx }](\cos (2x +3))$$
$$\frac{ dy }{ dx }=(3)(2)\cos (2x +3)$$
$$\frac{ dy }{ dx }=6\cos (2x +3)$$Do you understand?

calculusfunctions · Answer

@tenistaego, where did you go?