Solve r^3-4r^2+3r-12^2

$$r ^ { 3 } - 4 r ^ { 2 } + 3 r - 12 ^ { 2 }$$

Differentiate w.r.t. r

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

Steps Using Derivative Rule for Sum

Calculate 12 to the power of 2 and get 144.

$$\frac{\mathrm{d}}{\mathrm{d}r}(r^{3}-4r^{2}+3r-144)$$

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}.

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

Subtract 1 from 3.

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

Multiply 2 times -4.

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

Subtract 1 from 2.

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

Subtract 1 from 1.

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

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

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

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

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

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

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

Evaluate

$$r^{3}-4r^{2}+3r-144$$

Solution Steps

Calculate 12 to the power of 2 and get 144.

$$r^{3}-4r^{2}+3r-144$$