Solve (x^{2})^3div[(x^9divx^7)*x^2]

$$( x ^ { 2 } ) ^ { 3 } \div [ ( x ^ { 9 } \div x ^ { 7 } ) \cdot x ^ { 2 } ]$$

Evaluate

$$x^{2}$$

Solution Steps

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

$$\frac{x^{6}}{\frac{x^{9}}{x^{7}}x^{2}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 9 to get 2.

$$\frac{x^{6}}{x^{2}x^{2}}$$

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

$$x^{2}$$

Differentiate w.r.t. x

$$2x$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{\frac{x^{9}}{x^{7}}x^{2}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 7 from 9 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}}{x^{2}x^{2}})$$

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

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

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 6 to get 2.

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

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

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

Subtract 1 from 2.

$$2x^{1}$$

For any term t, t^{1}=t.

$$2x$$