Solve 18x^-4x^-5/10x^3

$$\frac { 18 x ^ { - 4 } x ^ { - 5 } } { 10 x ^ { 3 } }$$

Evaluate

$$\frac{9}{5x^{12}}$$

Solution Steps

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

$$\frac{18x^{-9}}{10x^{3}}$$

Cancel out 2 in both numerator and denominator.

$$\frac{9x^{-9}}{5x^{3}}$$

To divide powers of the same base, subtract the numerator's exponent from the denominator's exponent.

$$\frac{9}{5x^{12}}$$

Differentiate w.r.t. x

$$-\frac{108}{5x^{13}}$$

Solution Steps

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{18}{10x^{5}}x^{-4-3})$$

Do the arithmetic.

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

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-7\times \frac{9}{5x^{5}}x^{-7-1}$$

Do the arithmetic.

$$\left(-\frac{63}{5x^{5}}\right)x^{-8}$$