Solve 2x^2*5x^5

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

Evaluate

$$10x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$2x^{7}\times 5$$

Multiply 2 and 5 to get 10.

$$10x^{7}$$

Differentiate w.r.t. x

$$70x^{6}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 5 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(2x^{7}\times 5)$$

Multiply 2 and 5 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(10x^{7})$$

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

$$7\times 10x^{7-1}$$

Multiply 7 times 10.

$$70x^{7-1}$$

Subtract 1 from 7.

$$70x^{6}$$