Solve 12x^-7*5x^-4

$$12 x ^ { - 7 } \cdot 5 x ^ { - 4 }$$

Evaluate

$$\frac{60}{x^{11}}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add -7 and -4 to get -11.

$$12x^{-11}\times 5$$

Multiply 12 and 5 to get 60.

$$60x^{-11}$$

Differentiate w.r.t. x

$$-\frac{660}{x^{12}}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add -7 and -4 to get -11.

$$\frac{\mathrm{d}}{\mathrm{d}x}(12x^{-11}\times 5)$$

Multiply 12 and 5 to get 60.

$$\frac{\mathrm{d}}{\mathrm{d}x}(60x^{-11})$$

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

$$-11\times 60x^{-11-1}$$

Multiply -11 times 60.

$$-660x^{-11-1}$$

Subtract 1 from -11.

$$-660x^{-12}$$