Solve 4z*2z^3

$$4z \times 2 { z }^{ 3 }$$

Evaluate

$$8z^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$4z^{4}\times 2$$

Multiply 4 and 2 to get 8.

$$8z^{4}$$

Differentiate w.r.t. z

$$32z^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 3 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}z}(4z^{4}\times 2)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}z}(8z^{4})$$

The derivative of ax^{n} is nax^{n-1}.

$$4\times 8z^{4-1}$$

Multiply 4 times 8.

$$32z^{4-1}$$

Subtract 1 from 4.

$$32z^{3}$$