Solve (x^2)^3xdivx^4

$$( x ^ { 2 } ) ^ { 3 } x \div x ^ { 4 }$$

Evaluate

$$x^{3}$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{x^{6}x}{x^{4}}$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{x^{7}}{x^{4}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

$$x^{3}$$

Differentiate w.r.t. x

$$3x^{2}$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 2 and 3 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}x}{x^{4}})$$

To multiply powers of the same base, add their exponents. Add 6 and 1 to get 7.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{4}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 7 to get 3.

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

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

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

Subtract 1 from 3.

$$3x^{2}$$