Solve 2x*4x^3

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

Evaluate

$$8x^{4}$$

Solution Steps

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

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

Multiply 2 and 4 to get 8.

$$8x^{4}$$

Differentiate w.r.t. x

$$32x^{3}$$

Steps Using Definition of a Derivative

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

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

Multiply 2 and 4 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{4})$$

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

$$4\times 8x^{4-1}$$

Multiply 4 times 8.

$$32x^{4-1}$$

Subtract 1 from 4.

$$32x^{3}$$