2007-07-02 09:46:42 · 6 answers · asked by hakanak86 1 in Science & Mathematics ➔ Mathematics
Chain rule and power rule
d/dx(f(x))^2 = 2*f(x)*d/dx(f(x)) = 2*sin(x)*d/dx(sin(x)) = 2*sin(x)*cos(x)
Or you could use a trig identity. You could substitute
sin^2(x) = 1/2*(1-cos(2x)) then
d/dx(sin^2(x)) = d/dx(1/2*(1-cos(2x))) = d/dx(-1/2*cos(2x)) = sin(2x)
2007-07-02 10:29:07 · answer #1 · answered by Anonymous · 0⤊ 0⤋
D/dx(sin²x)=2sin x cos x
2007-07-02 16:56:36 · answer #2 · answered by yupchagee 7 · 0⤊ 0⤋
d/dx sin^2(x)
= 2 sin(x)^(2 - 1) d/dx (sin(x))
= 2 sin(x) d/dx (sin(x))
derivative of sin(x) is cos(x)
= 2 sin(x) cos(x)
double angle formula
= sin(2x)
2007-07-02 16:51:24 · answer #3 · answered by Ha!! 2 · 0⤊ 0⤋
just use the chain rule to get:
2*sinx*cosx dx
2007-07-02 16:50:38 · answer #4 · answered by grompfet 5 · 0⤊ 0⤋
d/dx(sin²x)
= d/dx (sinx* sinx)
= sinx*cosx +sinx *cosx
= 2sinxcosx = sin (2x)
2007-07-02 16:54:30 · answer #5 · answered by ironduke8159 7 · 0⤊ 0⤋
-2sinxcosx
2007-07-02 16:50:31 · answer #6 · answered by Larrymore 3 · 0⤊ 1⤋