Let the function y = sin (x ^ 2-1), then dy=

Let the function y = sin (x ^ 2-1), then dy=

dy=
cos(x^2-1)(x^2-1)'dx
=cos(x^2-1)*2xdx
=2xcos(x^2-1)dx

Let the function y = SiN x / E to the power of X, find dy

dy=[(cosx-sinx)/e^x]*dx

Find the differential dy of function y = cos (x ^ 2) · sin ^ 2 (1 / x)

y=cos（x^2）·sin^2（1/x）y'=-2xsin（x ²） sin ² （1/x）＋cos（x ²） 2sin1/x cos1/x ·-1/x ² =- 2xsin（x ²） sin ² （1/x）-1/x ² cos（x ²） Sin2 / x, so dy = [- 2xsin (x ²） si...

Find the differential dy of function y = sin ^ 3x when x = Π / 3 and △ x = 0.01

dy=3sin^2xcosxdx
When x = Π / 3 and △ x = 0.01, Dy = 3 * (3 / 4) * (1 / 2) * 0.01 = 0.01125

According to the differential law of composite function y-sin (2x + 1), find dy

y=sin(2x+1)
dy=dsin(2x+1)
=cos(2x+1)d(2x+1)
=2cos(2x+1)dx

Let the function y (x) be determined by the equation xcosy + ylnx = 0, then dy / DX =? Please write down the process and reason

Using the implicit function derivation rule: note that y is a function of X, and there are differences in the derivation of X on both sides of the equation
（x)'cos y+x(cosy)'+(y)'lnx+y(lnx)'=0
Namely
cos y-x (siny) y'+y'lnx+y (1/x)=0,
Y 'is obtained by solving the above equation