unfold fwdDeriv
R : Type u_3
C : Type u_1
inst✝² : Scalar R C
W : Type u_2
inst✝¹ : Vec C W
U : Type ?u.8066
inst✝ : SemiInnerProductSpace C U
x : W → C
hx : CDifferentiable C x
⊢ (fwdDeriv C fun w => cos (x w)) = fun w dw =>
    let xdx := fwdDeriv C x w dw;
    let s := sin xdx.1;
    let c := cos xdx.1;
    (c, xdx.2 * -s)
R : Type u_3
C : Type u_1
inst✝² : Scalar R C
W : Type u_2
inst✝¹ : Vec C W
U : Type ?u.8066
inst✝ : SemiInnerProductSpace C U
x : W → C
hx : CDifferentiable C x
⊢ (fun x_1 dx => ((fun w => cos (x w)) x_1, cderiv C (fun w => cos (x w)) x_1 dx)) = fun w dw =>
    let xdx := (x w, cderiv C x w dw);
    let s := sin xdx.1;
    let c := cos xdx.1;
    (c, xdx.2 * -s)