Solve (x^3)^2*x/x^5

$$\frac { ( x ^ { 3 } ) ^ { 2 } \cdot x } { x ^ { 5 } }$$

Evaluate

$$x^{2}$$

Solution Steps

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

$$\frac{x^{6}x}{x^{5}}$$

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

$$\frac{x^{7}}{x^{5}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 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 3 and 2 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{6}x}{x^{5}})$$

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{7}}{x^{5}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 5 from 7 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.

$$2x$$