Question

Помогите пожалуйста! Найти производную функции.

Answer 1

$(e^{x})'=e^x\\(x^{n})'=n*x^{n-1}\\(\sqrt{x})'=(x^{\frac{1}{2}})'=\frac{1}{2}x^{-\frac{1}{2}}=\frac{1}{2\sqrt{x}}\\(tg(x))'=\frac{1}{cos^2x}\\(u(v))'=u'(v)*v'$




$y'=(\frac{e^{-x^2}}{x-3})'+(\sqrt{tg(x)})'=\\=\frac{(e^{-x^2})'*(x-3)-(e^{-x^2})*(x-3)'}{(x-3)^2}+\frac{1}{2\sqrt{tg(x)}}*(tgx))'=\\=\frac{e^{-x^2}*(x^2)'*(x-3)-(e^{-x^2})*1}{(x-3)^2}+\frac{1}{2\sqrt{tg(x)}}*\frac{1}{cos^2(x)}=\\=\frac{e^{-x^2}(2x*(x-3)-1)}{(x-3)^2}+\frac{1}{2cos^2(x)*\sqrt{tg(x)}}$

Answer 2

Finding the Derivative of a Function

To find the derivative of the function y=(1/3)x^3-2x^2, we can use the rules of differentiation. The derivative of a function represents the rate of change of the function with respect to its variable.

The derivative of the given function can be found as follows:

y=(1/3)x^3-2x^2

The derivative of the function y with respect to x, denoted as y', is calculated as follows:

y' = (1/3)(3)x^(3-1) - 2(2)x^(2-1)

y' = x^2 - 4x

Therefore, the derivative of the function y=(1/3)x^3-2x^2 with respect to x is y' = x^2 - 4x.