`g(alpha) = 5^(-alpha/2)sin(2alpha)` Find the derivative of the function

Monday, October 28, 2013

$\displaystyle{g{{\left(\alpha\right)}}}={{5}}^{{-\frac{\alpha}{{2}}}}{\sin{{\left({2}\alpha\right)}}}$ Find the derivative of the function

We shall use:

Product rule

$\displaystyle{\left({f{{\left({x}\right)}}}{g{{\left({x}\right)}}}\right)}'={f{'}}{\left({x}\right)}{g{{\left({x}\right)}}}+{f{{\left({x}\right)}}}{g{'}}{\left({x}\right)}$

Chain rule

$\displaystyle{\left({f{{\left({g{{\left({x}\right)}}}\right)}}}\right)}'={f{'}}{\left({g{{\left({x}\right)}}}\right)}{g{'}}{\left({x}\right)}$

First we apply product rule.

$\displaystyle{g{'}}{\left(\alpha\right)}={\left({{5}}^{{-\frac{\alpha}{{2}}}}\right)}'{\sin{{\left({2}\alpha\right)}}}+{{5}}^{{-\frac{\alpha}{{2}}}}{\left({\sin{{\left({2}\alpha\right)}}}\right)}'=$

Now we apply chain rule to the composite functions we need to derivate.

$\displaystyle{{5}}^{{-\frac{\alpha}{{2}}}}{\ln{{\left({5}\right)}}}\cdot{\left(-\frac{{1}}{{2}}\right)}{\sin{{\left({2}\alpha\right)}}}+{{5}}^{{-\frac{\alpha}{{2}}}}{\cos{{\left({2}\alpha\right)}}}\cdot{2}$

Blog

Monday, October 28, 2013

$\displaystyle{g{{\left(\alpha\right)}}}={{5}}^{{-\frac{\alpha}{{2}}}}{\sin{{\left({2}\alpha\right)}}}$ Find the derivative of the function

No comments:

Post a Comment

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

Monday, October 28, 2013

Find the derivative of the function

No comments:

Post a Comment

Thomas Jefferson&#39;s election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?

$\displaystyle{g{{\left(\alpha\right)}}}={{5}}^{{-\frac{\alpha}{{2}}}}{\sin{{\left({2}\alpha\right)}}}$ Find the derivative of the function

Thomas Jefferson's election in 1800 is sometimes called the Revolution of 1800. Why could it be described in this way?