Solve dx/+x^4

$$\frac { d x } { + x ^ { 4 } }$$

Differentiate w.r.t. x

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

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{d}{1}x^{1-4})$$

Do the arithmetic.

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

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}.

$$-3dx^{-3-1}$$

Do the arithmetic.

$$\left(-3d\right)x^{-4}$$

Evaluate

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

Solution Steps

Cancel out x in both numerator and denominator.

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