Whakaoti i te dh=(1.5t+6)dt

$$d h = ( 1.5 t + 6 ) d t$$

Whakaoti mō d

$$\left\{\begin{matrix}\\d=0\text{, }&\text{unconditionally}\\d\in \mathrm{R}\text{, }&h=t\left(\frac{3t}{2}+6\right)\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5t+6 ki te d.

$$dh=\left(1.5td+6d\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5td+6d ki te t.

$$dh=1.5dt^{2}+6dt$$

Tangohia te 1.5dt^{2} mai i ngā taha e rua.

$$dh-1.5dt^{2}=6dt$$

Tangohia te 6dt mai i ngā taha e rua.

$$dh-1.5dt^{2}-6dt=0$$

Pahekotia ngā kīanga tau katoa e whai ana i te d.

$$\left(h-1.5t^{2}-6t\right)d=0$$

He hanga arowhānui tō te whārite.

$$\left(-\frac{3t^{2}}{2}+h-6t\right)d=0$$

Whakawehe 0 ki te -1.5t^{2}-6t+h.

$$d=0$$

Whakaoti mō h

$$\left\{\begin{matrix}\\h=t\left(\frac{3t}{2}+6\right)\text{, }&\text{unconditionally}\\h\in \mathrm{R}\text{, }&d=0\end{matrix}\right.$$

Ngā Upane mō te Whakaoti Whārite Rārangi

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5t+6 ki te d.

$$dh=\left(1.5td+6d\right)t$$

Whakamahia te āhuatanga tohatoha hei whakarea te 1.5td+6d ki te t.

$$dh=1.5dt^{2}+6dt$$

He hanga arowhānui tō te whārite.

$$dh=\frac{3dt^{2}}{2}+6dt$$

Whakawehea ngā taha e rua ki te d.

$$\frac{dh}{d}=\frac{dt\left(\frac{3t}{2}+6\right)}{d}$$

Mā te whakawehe ki te d ka wetekia te whakareanga ki te d.

$$h=\frac{dt\left(\frac{3t}{2}+6\right)}{d}$$

Whakawehe dt\left(6+\frac{3t}{2}\right) ki te d.

$$h=\frac{3t\left(t+4\right)}{2}$$