Solve 5x^4*6x^3

$$5 { x }^{ 4 } \times 6 { x }^{ 3 }$$

Evaluate

$$30x^{7}$$

Solution Steps

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

$$5x^{7}\times 6$$

Multiply 5 and 6 to get 30.

$$30x^{7}$$

Differentiate w.r.t. x

$$210x^{6}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{7}\times 6)$$

Multiply 5 and 6 to get 30.

$$\frac{\mathrm{d}}{\mathrm{d}x}(30x^{7})$$

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

$$7\times 30x^{7-1}$$

Multiply 7 times 30.

$$210x^{7-1}$$

Subtract 1 from 7.

$$210x^{6}$$