Solve x^2*22x*121

$${ x }^{ 2 } \times 22x \times 121$$

Evaluate

$$2662x^{3}$$

Solution Steps

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

$$x^{3}\times 22\times 121$$

Multiply 22 and 121 to get 2662.

$$x^{3}\times 2662$$

Differentiate w.r.t. x

$$7986x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 22\times 121)$$

Multiply 22 and 121 to get 2662.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\times 2662)$$

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

$$3\times 2662x^{3-1}$$

Multiply 3 times 2662.

$$7986x^{3-1}$$

Subtract 1 from 3.

$$7986x^{2}$$