How do i find the derivative of 3pi Sec^3[Pi x]Tan[Pi x]?

Question

solomonzelman · Answer

$\LARGE\color{blue}{ 3π\sec^3(πx)\tan(πx)   }$


$\LARGE\color{blue}{ 3π\frac{1}{\cos^3(πx)}\frac{\sin(πx)}{\cos(πx)}   }$


$\LARGE\color{blue}{ \frac{3π\sin(πx)}{\cos^4(πx)}   }$

this is the f(x).

solomonzelman · Answer

(Refresh when you see weird things with question marks)

solomonzelman · Answer

$\LARGE\color{blue}{ \frac{3π\sin(πx)}{\cos^4(πx)}   }$

take the derivative of 

$\LARGE\color{blue}{ \frac{\sin(πx)}{\cos^4(πx)}   }$

and multiply times 3pi.


$\LARGE\color{blue}{ \frac{\sin(πx)}{\cos^4(πx)}   }$

d/dx is going to be:

$\LARGE\color{blue}{ \frac{cos^4(πx)~π\cos(πx)-4π\sin^3(πx)~\sin(πx)}{\cos^8(πx)}   }$

solomonzelman · Answer

$\LARGE\color{blue}{ \frac{πcos^5(πx)-4π\sin^4(πx)}{\cos^8(πx)}   }$

solomonzelman · Answer

you have to REFRESH if you see wired rhombuses with question marks.