Solve 4n^4*2n^-3

$$4 n ^ { 4 } \cdot 2 n ^ { - 3 }$$

Evaluate

$$8n$$

Solution Steps

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

$$4n^{1}\times 2$$

Calculate n to the power of 1 and get n.

$$4n\times 2$$

Multiply 4 and 2 to get 8.

$$8n$$

Differentiate w.r.t. n

$$8$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n^{1}\times 2)$$

Calculate n to the power of 1 and get n.

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

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}n}(8n)$$

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

$$8n^{1-1}$$

Subtract 1 from 1.

$$8n^{0}$$

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

$$8\times 1$$

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

$$8$$