jutskaputska

Lause
D\sin x=\cos x
D\cos x=-\sin x
 
esimerkki
määritä
a)
f'\left(x\right), kun f\left(x\right)=2\sin x+\cos x
f'\left(x\right)=2\cos x-\sin x
b)
f'\left(\frac{\pi}{2}\right){,}\ kun\ f\left(x\right)=\sin x-3\cos x
f'\left(x\right)=\cos x+3\sin x
f'\left(\frac{\pi}{2}\right)=0+3\cdot1=3
 
esimerkki
derivoi
a)
h\left(x\right)=x^3\cos x
h'\left(x\right)=3x^2\cos x-x^3\sin x
b)
h\left(x\right)=\frac{\sin x}{\cos x}
h'\left(x\right)=\frac{f'\left(x\right)g\left(x\right)-f\left(x\right)g'\left(x\right)}{\left(g\left(x\right)\right)^2}=\frac{\cos^2x+\sin^2x}{\cos^2x}=\frac{1}{\cos^2x}