Solve x*x^4-3x^7:x^2

$$x \cdot x ^ { 4 } - 3 x ^ { 7 } : x ^ { 2 }$$

Evaluate

$$-2x^{5}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$x^{5}-\frac{3x^{7}}{x^{2}}$$

Cancel out x^{2} in both numerator and denominator.

$$x^{5}-3x^{5}$$

Combine x^{5} and -3x^{5} to get -2x^{5}.

$$-2x^{5}$$

Differentiate w.r.t. x

$$-10x^{4}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 1 and 4 to get 5.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}-\frac{3x^{7}}{x^{2}})$$

Cancel out x^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{5}-3x^{5})$$

Combine x^{5} and -3x^{5} to get -2x^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-2x^{5})$$

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

$$5\left(-2\right)x^{5-1}$$

Multiply 5 times -2.

$$-10x^{5-1}$$

Subtract 1 from 5.

$$-10x^{4}$$