Solve 25x^2div5x^-4

$$25 x ^ { 2 } \div 5 x ^ { - 4 }$$

Evaluate

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

Solution Steps

Divide 25x^{2} by 5 to get 5x^{2}.

$$5x^{2}x^{-4}$$

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

$$5x^{-2}$$

Differentiate w.r.t. x

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

Steps Using Definition of a Derivative

Divide 25x^{2} by 5 to get 5x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}x^{-4})$$

To multiply powers of the same base, add their exponents. Add 2 and -4 to get -2.

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

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

$$-2\times 5x^{-2-1}$$

Multiply -2 times 5.

$$-10x^{-2-1}$$

Subtract 1 from -2.

$$-10x^{-3}$$