Solve 4x*16x^2=

$$4x \times 16 { x }^{ 2 } =$$

Evaluate

$$64x^{3}$$

Solution Steps

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

$$4x^{3}\times 16$$

Multiply 4 and 16 to get 64.

$$64x^{3}$$

Differentiate w.r.t. x

$$192x^{2}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\times 16)$$

Multiply 4 and 16 to get 64.

$$\frac{\mathrm{d}}{\mathrm{d}x}(64x^{3})$$

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

$$3\times 64x^{3-1}$$

Multiply 3 times 64.

$$192x^{3-1}$$

Subtract 1 from 3.

$$192x^{2}$$