Solve 2^6+14z^3+49

$${ 2 }^{ 6 } +14 { z }^{ 3 } +49$$

Evaluate

$$14z^{3}+113$$

Solution Steps

Calculate 2 to the power of 6 and get 64.

$$64+14z^{3}+49$$

Add 64 and 49 to get 113.

$$113+14z^{3}$$

Differentiate w.r.t. z

$$42z^{2}$$

Steps Using Derivative Rule for Sum

Calculate 2 to the power of 6 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}z}(64+14z^{3}+49)$$

Add 64 and 49 to get 113.

$$\frac{\mathrm{d}}{\mathrm{d}z}(113+14z^{3})$$

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}.

$$3\times 14z^{3-1}$$

Multiply 3 times 14.

$$42z^{3-1}$$

Subtract 1 from 3.

$$42z^{2}$$