Tentukan turunan dari y= x³. cos 7x

Tentukan turunan dari y= x³. cos 7x

Jawab:

y = x³ cos x

u = x³ ==> u' = 3x²

v = cos x ==> v' = – sin x

y' = u'v + uv'

y' = 3x² cos x + x³.-sin x

y' = 3x² cos x – x³ sin x

Jawab :

$3x^2cos{7x}-7x^3sin{7x}$

Cara Pengerjaan :

$y=x^3cos{7x}\\frac{dy}{dx}=frac{d}{dx}(x^3cos{7x})=?$

Ingat !

$frac{d}{dx}(UV)=U'V+UV'$

Maka,

$x^3cos{7x}$

U = $x^3$

V = $cos{7x}$

$frac{d}{dx}(x^3cos{7x})=(frac{d}{dx}x^3)timescos{7x}+x^3times(frac{d}{dx}cos{7x})\$

Ingat !

1) $frac{d}{dx}(ax^n)=atimes ntimes x^{n-1}$

2) $frac{d}{dx}cos{(ax)}=-asin{ax}$

Maka,

$frac{d}{dx}(x^3cos{7x})=(frac{d}{dx}x^3)timescos{7x}+x^3times(frac{d}{dx}cos{7x})\\frac{d}{dx}(x^3cos{7x})=(3x^2)timescos{7x}+x^3times(-7sin{7x})\\frac{d}{dx}(x^3cos{7x})=3x^2cos{7x}-7x^3sin{7x}$