a^3-4a^2+2a-1-এর সমাধান করুন

$$a ^ { 3 } - 4 a ^ { 2 } + 2 a - 1$$

Differentiate w.r.t. a

$$3a^{2}-8a+2$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$3a^{3-1}+2\left(-4\right)a^{2-1}+2a^{1-1}$$

Subtract 1 from 3.

$$3a^{2}+2\left(-4\right)a^{2-1}+2a^{1-1}$$

Multiply 2 times -4.

$$3a^{2}-8a^{2-1}+2a^{1-1}$$

Subtract 1 from 2.

$$3a^{2}-8a^{1}+2a^{1-1}$$

Subtract 1 from 1.

$$3a^{2}-8a^{1}+2a^{0}$$

For any term t, t^{1}=t.

$$3a^{2}-8a+2a^{0}$$

For any term t except 0, t^{0}=1.

$$3a^{2}-8a+2\times 1$$

For any term t, t\times 1=t and 1t=t.

$$3a^{2}-8a+2$$

Evaluate

$$a^{3}-4a^{2}+2a-1$$