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

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

Evalwa

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

Passi għall-Użu ta' Regola Derivattiva għal Somma

Espandi \frac{1}{1.5} billi timmultiplika kemm in-numeratur kif ukoll id-denominatur b'10.

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

Naqqas il-frazzjoni \frac{10}{15} għat-termini l-aktar baxxi billi testratta u tikkanċella barra 5.

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

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

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

Ikkalkula \frac{2}{3} bil-power ta' 10 u tikseb \frac{1024}{59049}.

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

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

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

Ikkalkula 1.5 bil-power ta' 2 u tikseb 2.25.

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

Id-derivattiva ta’ polynomial hija s-somma tad-derivattivi tat-termini tagħha. Id-derivattiva ta’ terminu kostanti hija 0. Id-derivattiva ta’ ax^{n} hijanax^{n-1}.

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

Immultiplika 10 b'\frac{1024}{59049}.

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

Naqqas 1 minn 10.

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

Immultiplika 2 b'-2.25.

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

Naqqas 1 minn 2.

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

Għal kwalunkwe terminu t, t^{1}=t.

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

Iddifferenzja w.r.t. x

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