Solve 4x^2*2x^5*3x^-2

$$4 { x }^{ 2 } \times 2 { x }^{ 5 } \times 3 { x }^{ -2 }$$

Evaluate

$$24x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$4x^{7}\times 2\times 3x^{-2}$$

To multiply powers of the same base, add their exponents. Add 7 and -2 to get 5.

$$4x^{5}\times 2\times 3$$

Multiply 4 and 2 to get 8.

$$8x^{5}\times 3$$

Multiply 8 and 3 to get 24.

$$24x^{5}$$

Differentiate w.r.t. x

$$120x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7}\times 2\times 3x^{-2})$$

To multiply powers of the same base, add their exponents. Add 7 and -2 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{5}\times 2\times 3)$$

Multiply 4 and 2 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(8x^{5}\times 3)$$

Multiply 8 and 3 to get 24.

$$\frac{\mathrm{d}}{\mathrm{d}x}(24x^{5})$$

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

$$5\times 24x^{5-1}$$

Multiply 5 times 24.

$$120x^{5-1}$$

Subtract 1 from 5.

$$120x^{4}$$