\(dy/dt=((e^(2t)+1)(te^t+e^t)-(te^t+2)(2e^(2t)))/((e^(2t)+1)^2)\)

\(=((1-t)e^(3t)-4e^(2t)+(1+t)e^t)/((e^(2t)+1)^2)\)

\(=((1-t)e^(3t)-4e^(2t)+(1+t)e^t)/((e^(2t)+1)^2)\)

Question

asked 2020-12-28

Find derivatives of the functions defined as follows.
\(y=(t^2 e^(2t))/(t+e^(3t))\)

asked 2021-03-09

Find derivatives of the functions defined as follows.
\(f(x)=e^(x sqrt(3x+2))\)

asked 2021-01-06

Find derivatives of the functions defined as follows.
\(\displaystyle f{{\left({x}\right)}}={e}^{{\frac{{x}^{2}}{{{x}^{3}+{2}}}}}\)

asked 2020-12-21

Find derivatives of the functions defined as follows.
\(s=2*3^(sqrt t)\)

asked 2021-03-05

Find derivatives of the functions defined as follows.
\(s=5*2^(sqrt(t-2))\)

asked 2020-11-08

Find derivatives of the functions defined as follows.
y=4^(-5x+2)

asked 2021-03-06

Find derivatives of the functions defined as follows.
\(y=3*4^(x^2+2)\)

asked 2020-10-23

Find derivatives of the functions defined as follows.
\(y= -10^(3x^2-4)\(

asked 2020-11-11

Calculating derivatives Find the derivative of the following functions.

\(\displaystyle{y}={{\cos}^{{2}}{x}}\)

\(\displaystyle{y}={{\cos}^{{2}}{x}}\)

asked 2021-03-09

Find the first partial derivatives of the following functions.

\(\displaystyle{s}{\left({y},{z}\right)}={z}^{{2}}{\tan{{y}}}{z}\)

\(\displaystyle{s}{\left({y},{z}\right)}={z}^{{2}}{\tan{{y}}}{z}\)