Homework SourseCompute the following derivatives show work a fxsinepi b fx
Compute the following derivatives, show work !:
a) f(x)=sin(e^pi)
b) f(x) = (sqrt(sin(x^2-3x)+x))/(ln^2(x)
c) f(x)= (1+x)^(x^2)
d) y(x) is given by sin(xy^2)-cos(y)=1
a) f(x)=sin(e^pi)
b) f(x) = (sqrt(sin(x^2-3x)+x))/(ln^2(x)
c) f(x)= (1+x)^(x^2)
d) y(x) is given by sin(xy^2)-cos(y)=1
Solution
a . f(X) const so =0 b.d/dx(sqrt(sin(x^2-3 x)+x)/(log^2(x))) = (x (log(x)-4)-4 sin((x-3) x)+x (2 x-3) log(x) cos((x-3) x))/(2 x log^3(x) sqrt(x+sin((x-3) x)))(apply derivative of u/v formula=(vdu-udv)/v^2) c.d/dx((1+x)^(x^2)) = x (x+1)^(x^2-1) (x+2 (x+1) log(x+1)) x^2*D(1+x)*D(x^2) d.
