Question

найдите значение производной функции в заданной точке: f(x)=2x-3/sin x ,x=п/4​

Answer 1

f'(x)=((2x-3)'*sinx-(2x-3)*(sinx)')/sin²x=(2*sinx-(2x-3)*cosx)/sin²x=

=(2*sin(π/4)-((2*π/4)-3)*cos(π/4))/sin²(π/4)=

=(2*√2/2-(π/2-3)*√2/2)/(√2/2)²=(√2-√2*(π/2-3)/2)/(1/2)=

=2*(2*√2-√2*(π/2-3)/2=√2*(2-π/2+3)=√2*(5-π/2).