Solve [frac{(x^{7}*x^3):x^2}{x^4}]:x^3

$$[ \frac { ( x ^ { 7 } \cdot x ^ { 3 } ) : x ^ { 2 } } { x ^ { 4 } } ] : x ^ { 3 }$$

Evaluate

$$x$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\frac{\frac{x^{10}}{x^{2}}}{x^{4}}}{x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$\frac{\frac{x^{8}}{x^{4}}}{x^{3}}$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 8 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

$$1$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 7 and 3 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{\frac{x^{10}}{x^{2}}}{x^{4}}}{x^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 2 from 10 to get 8.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{\frac{x^{8}}{x^{4}}}{x^{3}})$$

To divide powers of the same base, subtract the denominator's exponent from the numerator's exponent. Subtract 4 from 8 to get 4.

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

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

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

Calculate x to the power of 1 and get x.

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

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

$$x^{1-1}$$

Subtract 1 from 1.

$$x^{0}$$

For any term t except 0, t^{0}=1.

$$1$$