Solve 9x^10*5x^-4

$$9 x ^ { 10 } \cdot 5 x ^ { - 4 }$$

Evaluate

$$45x^{6}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and -4 to get 6.

$$9x^{6}\times 5$$

Multiply 9 and 5 to get 45.

$$45x^{6}$$

Differentiate w.r.t. x

$$270x^{5}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 10 and -4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(9x^{6}\times 5)$$

Multiply 9 and 5 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{6})$$

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

$$6\times 45x^{6-1}$$

Multiply 6 times 45.

$$270x^{6-1}$$

Subtract 1 from 6.

$$270x^{5}$$