Solve 4x^2*2x^2*3x^-2

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

Evaluate

$$24x^{2}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

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

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

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

Multiply 4 and 2 to get 8.

$$8x^{2}\times 3$$

Multiply 8 and 3 to get 24.

$$24x^{2}$$

Differentiate w.r.t. x

$$48x$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}\times 2\times 3x^{-2})$$

To multiply powers of the same base, add their exponents. Add 4 and -2 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{2}\times 2\times 3)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{2}\times 3)$$

Multiply 8 and 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{2})$$

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

$$2\times 24x^{2-1}$$

Multiply 2 times 24.

$$48x^{2-1}$$

Subtract 1 from 2.

$$48x^{1}$$

For any term t, t^{1}=t.

$$48x$$