Solve 1/x^2*1/x

$$\frac{ 1 }{ { x }^{ 2 } } \times \frac{ 1 }{ x }$$

Evaluate

$$\frac{1}{x^{3}}$$

Solution Steps

Multiply \frac{1}{x^{2}} times \frac{1}{x} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1}{x^{2}x}$$

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{1}{x^{3}}$$

Differentiate w.r.t. x

$$-\frac{3}{x^{4}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{1}{1}x^{-1-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{-3})$$

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}.

$$-3x^{-3-1}$$

Do the arithmetic.

$$-3x^{-4}$$