if-df-dx-f-what-are-the-value-of-d-dx-Q3707-

Question Number 3764 by 123456 last updated on 19/Dec/15

if \frac{d f}{d x} = f, what are the value of

\frac{d θ}{d x} ? (Q 3707)

Commented by Filup last updated on 19/Dec/15

Attempt :

\frac{d θ}{d x} = \frac{\frac{d^{2} f}{{d x}^{2}}}{1 + {(\frac{d f}{d x})}^{2}}

{(\frac{d f}{d x})}^{2} = f^{2}

\frac{d^{2} f}{{d x}^{2}} = f^{'}

∴ \frac{d θ}{d x} = \frac{f^{'}}{1 + f^{2}}

Commented by prakash jain last updated on 20/Dec/15

\frac{d f}{d x} = f

f (x) = e^{x + c}

\tan θ = f^{'} (x) = e^{x + c}

\frac{d θ}{d x} = \frac{e^{x + c}}{1 + e^{2 x + 2 c}}