f(x)=e^-x · x^3 · tan(x)

What´s the derivative of the function?

Question

f(x)=e^-x · x^3 · tan(x)

What´s the derivative of the function?

sshayer · Answer

$$\frac{ d }{ dx }\left\{ u \left( vw \right) \right\}=u \prime(vw)+u(vw)\prime $$
$$=u \prime(vw)+u \left( vw \prime +v \prime w \right)$$

johnw · Answer

Is it possible to explain in English? :)

sshayer · Answer

u,v,w are functions of x

johnw · Answer

No, but you probably understand what I mean

sshayer · Answer

$$u=e ^{-x},v=x^3,w=\tan x$$

johnw · Answer

I can promise you both I´m more confused now than before your answers :)

The derivative for x^3 is 3x and for tan(x) it is 1/cos^2x right? I

sshayer · Answer

$$\frac{ d }{ dx }(e ^{-x})=e ^{-x}\frac{ d }{ dx }(-x)=?$$

johnw · Answer

Now we´re talking

johnw · Answer

Did he seriously remove his answers? I haven´t even given any medals yet? I don´t get it....

sshayer · Answer

$$f(x)=e^{-x}[x^3 \tan x]$$
$$f \prime(x)=e^{-x}[x^3\tan x]\prime +e^{-x}(-1)[x^3 \tan x]$$
$$=e^{-x}[x^3\sec ^2x+3x^2\tan x]-e^{-x}x^3 \tan x$$
$$=e^{-x}x^2[x \sec ^2x+3 \tan x-x \tan x  ]$$