Solve w^3-8w^2+41w-48

$$w ^ { 3 } - 8 w ^ { 2 } + 41 w - 48$$

Differentiate w.r.t. w

$$3w^{2}-16w+41$$

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}.

$$3w^{3-1}+2\left(-8\right)w^{2-1}+41w^{1-1}$$

Subtract 1 from 3.

$$3w^{2}+2\left(-8\right)w^{2-1}+41w^{1-1}$$

Multiply 2 times -8.

$$3w^{2}-16w^{2-1}+41w^{1-1}$$

Subtract 1 from 2.

$$3w^{2}-16w^{1}+41w^{1-1}$$

Subtract 1 from 1.

$$3w^{2}-16w^{1}+41w^{0}$$

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

$$3w^{2}-16w+41w^{0}$$

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

$$3w^{2}-16w+41\times 1$$

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

$$3w^{2}-16w+41$$

Evaluate

$$w^{3}-8w^{2}+41w-48$$