Solve x^3*x^4x^-3/x^3

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

Evaluate

$$x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$\frac{x^{7}x^{-3}}{x^{3}}$$

To multiply powers of the same base, add their exponents. Add 7 and -3 to get 4.

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 3 from 4 to get 1.

$$x^{1}$$

Calculate x to the power of 1 and get x.

$$x$$

Differentiate w.r.t. x

$$1$$

Solution Steps

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

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

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(xx^{0})$$

For any number a except 0, a^{0}=1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x)$$

The derivative of a constant term is 0.

$$0$$