Solve 4x^4(5x^3)

$$4 { x }^{ 4 } (5 { x }^{ 3 } )$$

Evaluate

$$20x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$4x^{7}\times 5$$

Multiply 4 and 5 to get 20.

$$20x^{7}$$

Differentiate w.r.t. x

$$140x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 3 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{7}\times 5)$$

Multiply 4 and 5 to get 20.

$$\frac{\mathrm{d}}{\mathrm{d}x}(20x^{7})$$

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

$$7\times 20x^{7-1}$$

Multiply 7 times 20.

$$140x^{7-1}$$

Subtract 1 from 7.

$$140x^{6}$$