Solve 14^3+15^3-sqrt[3]{4096}a

$$14 ^ { 3 } + 15 ^ { 3 } - \sqrt[ 3 ] { 4096 } a$$

Evaluate

$$6119-16a$$

Solution Steps

Calculate 14 to the power of 3 and get 2744.

$$2744+15^{3}-\sqrt[3]{4096}a$$

Calculate 15 to the power of 3 and get 3375.

$$2744+3375-\sqrt[3]{4096}a$$

Add 2744 and 3375 to get 6119.

$$6119-\sqrt[3]{4096}a$$

Calculate \sqrt[3]{4096} and get 16.

$$6119-16a$$

Differentiate w.r.t. a

$$-16$$

Steps Using Derivative Rule for Sum

Calculate 14 to the power of 3 and get 2744.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2744+15^{3}-\sqrt[3]{4096}a)$$

Calculate 15 to the power of 3 and get 3375.

$$\frac{\mathrm{d}}{\mathrm{d}a}(2744+3375-\sqrt[3]{4096}a)$$

Add 2744 and 3375 to get 6119.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6119-\sqrt[3]{4096}a)$$

Calculate \sqrt[3]{4096} and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}a}(6119-16a)$$

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}.

$$-16a^{1-1}$$

Subtract 1 from 1.

$$-16a^{0}$$

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

$$-16$$