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بسّط مشتقة القوة:
ddx[(1−x)4]\frac{d}{dx}\left[\left(1-x\right)^4\right]dxd[(1−x)4]
8(1+x)78\left(1+x\right)^78(1+x)7
4(1−x)34\left(1-x\right)^34(1−x)3
-4(1−x)34\left(1-x\right)^34(1−x)3
f(x)=x−3+2x−23+3f\left(x\right)=x^{-3}+2x^{-\frac{2}{3}}+3f(x)=x−3+2x−32+3
1x4+1x52\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}x41+x251
8(4−x)2\frac{8}{\left(4-x\right)^2}(4−x)28
−3(1x4+1x52)-3\left(\frac{1}{x^4}+\frac{1}{x^{\frac{5}{2}}}\right)−3(x41+x251)
ddt[(1+t2)10]\frac{d}{dt}\left[\left(1+t^2\right)^{10}\right]dtd[(1+t2)10]
20t(1+t2)920t\left(1+t^2\right)^920t(1+t2)9
(1+t2)2\left(1+t^2\right)^2(1+t2)2
6t (1+t2)2\left(1+t^2\right)^2(1+t2)2
ddx[x]\frac{d}{dx}\left[x\right]dxd[x]
sinx
cos2x
sin2x
ddx[5x3−3x2+10x−8]\frac{d}{dx}\left[5x^3-3x^2+10x-8\right]dxd[5x3−3x2+10x−8]
15x2−6x+1015x^2-6x+1015x2−6x+10
15x2−6x15x^2-6x15x2−6x
ddx[(1+x)8]\frac{d}{dx}\left[\left(1+x\right)^8\right]dxd[(1+x)8]
8x78x^78x7
12x312x^312x3
بسّط مشتقة القوة
ddx[x4+2x3+x2]\frac{d}{dx}\left[x^4+2x^3+x^2\right]dxd[x4+2x3+x2]
4(1+x)34\left(1+x\right)^34(1+x)3
4x3+6x2+2x4x^3+6x^2+2x4x3+6x2+2x
ddt[(1+t2)3]\frac{d}{dt}\left[\left(1+t^2\right)^3\right]dtd[(1+t2)3]
23
6t(1+t2)26t\left(1+t^2\right)^26t(1+t2)2
ddx[(1+x4)]\frac{d}{dx}\left[\left(1+x^4\right)\right]dxd[(1+x4)]
−4(1−x)3-4\left(1-x\right)^3−4(1−x)3
ddx[x544]\frac{d}{dx}\left[x^{544}\right]dxd[x544]
544x543544x^{543}544x543
544x542544x^{542}544x542
x543x^{543}x543
إنتهى الإختبار.