Solve 5x^4*2x^5

$$5 x ^ { 4 } \cdot 2 x ^ { 5 }$$

Evaluate

$$10x^{9}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$5x^{9}\times 2$$

Multiply 5 and 2 to get 10.

$$10x^{9}$$

Differentiate w.r.t. x

$$90x^{8}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 4 and 5 to get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{9}\times 2)$$

Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{9})$$

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

$$9\times 10x^{9-1}$$

Multiply 9 times 10.

$$90x^{9-1}$$

Subtract 1 from 9.

$$90x^{8}$$