Solve xx^2sqrt{9}

$$x { x }^{ 2 } \sqrt{ 9 }$$

Evaluate

$$3x^{3}$$

Solution Steps

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

$$x^{3}\sqrt{9}$$

Calculate the square root of 9 and get 3.

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

Differentiate w.r.t. x

$$9x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{3}\sqrt{9})$$

Calculate the square root of 9 and get 3.

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

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

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

Multiply 3 times 3.

$$9x^{3-1}$$

Subtract 1 from 3.

$$9x^{2}$$