Solve 36x*4x^2

$$36x \times 4 { x }^{ 2 }$$

Evaluate

$$144x^{3}$$

Solution Steps

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

$$36x^{3}\times 4$$

Multiply 36 and 4 to get 144.

$$144x^{3}$$

Differentiate w.r.t. x

$$432x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(36x^{3}\times 4)$$

Multiply 36 and 4 to get 144.

$$\frac{\mathrm{d}}{\mathrm{d}x}(144x^{3})$$

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

$$3\times 144x^{3-1}$$

Multiply 3 times 144.

$$432x^{3-1}$$

Subtract 1 from 3.

$$432x^{2}$$