Datrys d((1/1.5x)^10-(1.5x)^2+1)/dx

$$\frac { d ( ( \frac { 1 } { 1.5 } x ) ^ { 10 } - ( 1.5 x ) ^ { 2 } + 1 ) } { d x }$$

Enrhifo

$$x\left(\frac{10240x^{8}}{59049}-4.5\right)$$

Camau gan Ddefnyddio Rheol Deilliadol ar gyfer Swm

Ehangu \frac{1}{1.5} drwy luosi'r rhifiadur a'r enwadur gyda 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{10}{15}x\right)^{10}-\left(1.5x\right)^{2}+1)$$

Lleihau'r ffracsiwn \frac{10}{15} i'r graddau lleiaf posib drwy dynnu a chanslo allan 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{2}{3}x\right)^{10}-\left(1.5x\right)^{2}+1)$$

Ehangu \left(\frac{2}{3}x\right)^{10}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(\frac{2}{3}\right)^{10}x^{10}-\left(1.5x\right)^{2}+1)$$

Cyfrifo \frac{2}{3} i bŵer 10 a chael \frac{1024}{59049}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1024}{59049}x^{10}-\left(1.5x\right)^{2}+1)$$

Ehangu \left(1.5x\right)^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1024}{59049}x^{10}-1.5^{2}x^{2}+1)$$

Cyfrifo 1.5 i bŵer 2 a chael 2.25.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1024}{59049}x^{10}-2.25x^{2}+1)$$

Deilliad polynomaial yw swm deilliadau ei dermau. Deilliad term cyson yw 0. Y deilliad o ax^{n} yw nax^{n-1}.

$$10\times \frac{1024}{59049}x^{10-1}+2\left(-2.25\right)x^{2-1}$$

Lluoswch 10 â \frac{1024}{59049}.

$$\frac{10240}{59049}x^{10-1}+2\left(-2.25\right)x^{2-1}$$

Tynnu 1 o 10.

$$\frac{10240}{59049}x^{9}+2\left(-2.25\right)x^{2-1}$$

Lluoswch 2 â -2.25.

$$\frac{10240}{59049}x^{9}-4.5x^{2-1}$$

Tynnu 1 o 2.

$$\frac{10240}{59049}x^{9}-4.5x^{1}$$

Ar gyfer unrhyw derm t, t^{1}=t.

$$\frac{10240}{59049}x^{9}-4.5x$$

Gwahaniaethu w.r.t. x

$$\frac{10240x^{8}}{6561}-4.5$$