Solve 5x^4*9x^6

$$5 { x }^{ 4 } \times 9 { x }^{ 6 }$$

Evaluate

$$45x^{10}$$

Solution Steps

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

$$5x^{10}\times 9$$

Multiply 5 and 9 to get 45.

$$45x^{10}$$

Differentiate w.r.t. x

$$450x^{9}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{10}\times 9)$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{10})$$

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

$$10\times 45x^{10-1}$$

Multiply 10 times 45.

$$450x^{10-1}$$

Subtract 1 from 10.

$$450x^{9}$$