Solve 4n^2*4n^-2*n^2

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

Evaluate

$$16n^{2}$$

Solution Steps

Multiply n^{2} and n^{-2} to get 1.

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

Multiply 4 and 4 to get 16.

$$16n^{2}$$

Differentiate w.r.t. n

$$32n$$

Steps Using Definition of a Derivative

Multiply n^{2} and n^{-2} to get 1.

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

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}n}(16n^{2})$$

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

$$2\times 16n^{2-1}$$

Multiply 2 times 16.

$$32n^{2-1}$$

Subtract 1 from 2.

$$32n^{1}$$

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

$$32n$$