Solve =-a^3+3*4^2

$$= - a ^ { 3 } + 3 \cdot 4 ^ { 2 }$$

Evaluate

$$48-a^{3}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$-a^{3}+3\times 16$$

Multiply 3 and 16 to get 48.

$$-a^{3}+48$$

Differentiate w.r.t. a

$$-3a^{2}$$

Steps Using Derivative Rule for Sum

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{3}+3\times 16)$$

Multiply 3 and 16 to get 48.

$$\frac{\mathrm{d}}{\mathrm{d}a}(-a^{3}+48)$$

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}.

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

Multiply 3 times -1.

$$-3a^{3-1}$$

Subtract 1 from 3.

$$-3a^{2}$$