Solve 3x*3x^3

$$3 x \cdot 3 x ^ { 3 }$$

Evaluate

$$9x^{4}$$

Solution Steps

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

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

Multiply 3 and 3 to get 9.

$$9x^{4}$$

Differentiate w.r.t. x

$$36x^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 3 and 3 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{4})$$

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

$$4\times 9x^{4-1}$$

Multiply 4 times 9.

$$36x^{4-1}$$

Subtract 1 from 4.

$$36x^{3}$$