Solve 7x^4*5x^5=

$$7 x ^ { 4 } \cdot 5 x ^ { 5 } =$$

Evaluate

$$35x^{9}$$

Solution Steps

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

$$7x^{9}\times 5$$

Multiply 7 and 5 to get 35.

$$35x^{9}$$

Differentiate w.r.t. x

$$315x^{8}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(7x^{9}\times 5)$$

Multiply 7 and 5 to get 35.

$$\frac{\mathrm{d}}{\mathrm{d}x}(35x^{9})$$

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

$$9\times 35x^{9-1}$$

Multiply 9 times 35.

$$315x^{9-1}$$

Subtract 1 from 9.

$$315x^{8}$$