Differentiate
$\displaystyle y=(cosx)^{3x}$ with respect to x.
Using the basic differentiation rules for elementary functions, how do I approach this? What can be defined as u?
Is it $\displaystyle (cosx)^u$ or $\displaystyle u^{3x}$ ?
Differentiate
$\displaystyle y=(cosx)^{3x}$ with respect to x.
Using the basic differentiation rules for elementary functions, how do I approach this? What can be defined as u?
Is it $\displaystyle (cosx)^u$ or $\displaystyle u^{3x}$ ?
That's what I thought, but I've never applied logs to trig functions before, so i was hesitant. Thanx.
Difeerentiating
$\displaystyle \frac{d}{dx}(lny)=\frac{d}{dx}(3xlncosx)$
$\displaystyle \frac{y'}{y}=3x\frac{-sinx}{cosx}+3lncosx$
y=3xlncosx
$\displaystyle y'=9xlncosx(\frac{-xsinx}{cosx}+lncosx)$
Is this correct?
Let u = cos(x) and v = 3x
then differentiate $\displaystyle y= u^{v} $ by using the chain rule for functions of more than one variable
$\displaystyle \frac {dy}{dx} = \frac {\partial y}{\partial u} \ \frac {du}{dx} + \frac {\partial y}{\partial v} \ \frac {dv}{dx} $