Solve 4n*n*3n

$$4 n \cdot n \cdot 3 n$$

Evaluate

$$12n^{3}$$

Solution Steps

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

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

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$4n^{3}\times 3$$

Multiply 4 and 3 to get 12.

$$12n^{3}$$

Differentiate w.r.t. n

$$36n^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n^{2}\times 3n)$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}n}(4n^{3}\times 3)$$

Multiply 4 and 3 to get 12.

$$\frac{\mathrm{d}}{\mathrm{d}n}(12n^{3})$$

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

$$3\times 12n^{3-1}$$

Multiply 3 times 12.

$$36n^{3-1}$$

Subtract 1 from 3.

$$36n^{2}$$