Solve m(3)^2+24(3)-7

$$m ( 3 ) ^ { 2 } + 24 ( 3 ) - 7$$

Evaluate

$$9m+65$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$m\times 9+24\times 3-7$$

Multiply 24 and 3 to get 72.

$$m\times 9+72-7$$

Subtract 7 from 72 to get 65.

$$m\times 9+65$$

Differentiate w.r.t. m

$$9$$

Steps Using Derivative Rule for Sum

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m\times 9+24\times 3-7)$$

Multiply 24 and 3 to get 72.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m\times 9+72-7)$$

Subtract 7 from 72 to get 65.

$$\frac{\mathrm{d}}{\mathrm{d}m}(m\times 9+65)$$

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}.

$$9m^{1-1}$$

Subtract 1 from 1.

$$9m^{0}$$

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

$$9\times 1$$

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

$$9$$