?Ellip*

?EllipticE

fun1  = EllipticE[x]

?D

fun2  =  D[ EllipticE[x], x]

p1  =  Plot[fun1, {x, 0, 1}];

p2 =  Plot[fun2, {x, 0, 1}];

Show[p1, p2];

fun3  =  EllipticK[x]

fun4  =  D[EllipticK[x], x]

p3  = Plot[fun3, {x, 0, 1}];

p4 =  Plot[fun4, {x, 0, 1}];

Show[p3, p4];