Solve 9x^3*9x^2

$$9 x ^ { 3 } \cdot 9 x ^ { 2 }$$

Evaluate

$$81x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 9 and 9 to get 81.

$$81x^{5}$$

Differentiate w.r.t. x

$$405x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 2 to get 5.

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

Multiply 9 and 9 to get 81.

$$\frac{\mathrm{d}}{\mathrm{d}x}(81x^{5})$$

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

$$5\times 81x^{5-1}$$

Multiply 5 times 81.

$$405x^{5-1}$$

Subtract 1 from 5.

$$405x^{4}$$