Solve (5^3x^10)(5^3x^4)

$$( 5 ^ { 3 } x ^ { 10 } ) ( 5 ^ { 3 } x ^ { 4 } )$$

Evaluate

$$15625x^{14}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$5^{6}x^{10}x^{4}$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$5^{6}x^{14}$$

Calculate 5 to the power of 6 and get 15625.

$$15625x^{14}$$

Differentiate w.r.t. x

$$218750x^{13}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 3 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5^{6}x^{10}x^{4})$$

To multiply powers of the same base, add their exponents. Add 10 and 4 to get 14.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5^{6}x^{14})$$

Calculate 5 to the power of 6 and get 15625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(15625x^{14})$$

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

$$14\times 15625x^{14-1}$$

Multiply 14 times 15625.

$$218750x^{14-1}$$

Subtract 1 from 14.

$$218750x^{13}$$