I have some questions that I am struggling with understanding, can someone show the workings out and the answer to these please?
1.
If y=e^6x
Find d(e^6x)/d(x)
2.
Find d(sin(6x))/d(x)
+118723 1.
If y=e^6x
Find d(e^6x)/d(x)
$$\\y=e^{6x }\\\\
\frac{dy}{dx}=6e^{6x }$$
-------------------------------------------
$$\\\frac{d}{d(x)}(sin(6x))\\\\
=6cos(6x)\\\\\\
$let me see if I can do this formally using the chain rule$\\\\
y=sin(6x)\\\\
let\;\; u=6x \qquad so \qquad \frac{du}{dx}=6\\\\
y=sin(u)\qquad so \qquad \frac{dy}{du}=cos(u)\\\\
\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\\\\
\frac{dy}{dx}=cos(u)\times 6\\\\
\frac{dy}{dx}=cos(6x)\times 6\\\\
\frac{dy}{dx}=6cos(6x)\\\\$$
+118723 1.
If y=e^6x
Find d(e^6x)/d(x)
$$\\y=e^{6x }\\\\
\frac{dy}{dx}=6e^{6x }$$
-------------------------------------------
$$\\\frac{d}{d(x)}(sin(6x))\\\\
=6cos(6x)\\\\\\
$let me see if I can do this formally using the chain rule$\\\\
y=sin(6x)\\\\
let\;\; u=6x \qquad so \qquad \frac{du}{dx}=6\\\\
y=sin(u)\qquad so \qquad \frac{dy}{du}=cos(u)\\\\
\frac{dy}{dx}=\frac{dy}{du}\times \frac{du}{dx}\\\\
\frac{dy}{dx}=cos(u)\times 6\\\\
\frac{dy}{dx}=cos(6x)\times 6\\\\
\frac{dy}{dx}=6cos(6x)\\\\$$
