Solve -105x^3/3x^4

$$\frac { - 105 x ^ { 3 } } { 3 x ^ { 4 } }$$

Evaluate

$$-\frac{35}{x}$$

Steps for the Product of Two Exponentials

Use the rules of exponents to simplify the expression.

$$\left(-105x^{3}\right)^{1}\times \frac{1}{3x^{4}}$$

To raise the product of two or more numbers to a power, raise each number to the power and take their product.

$$\left(-105\right)^{1}\left(x^{3}\right)^{1}\times \frac{1}{3}\times \frac{1}{x^{4}}$$

Use the Commutative Property of Multiplication.

$$\left(-105\right)^{1}\times \frac{1}{3}\left(x^{3}\right)^{1}\times \frac{1}{x^{4}}$$

To raise a power to another power, multiply the exponents.

$$\left(-105\right)^{1}\times \frac{1}{3}x^{3}x^{4\left(-1\right)}$$

Multiply 4 times -1.

$$\left(-105\right)^{1}\times \frac{1}{3}x^{3}x^{-4}$$

To multiply powers of the same base, add their exponents.

$$\left(-105\right)^{1}\times \frac{1}{3}x^{3-4}$$

Add the exponents 3 and -4.

$$\left(-105\right)^{1}\times \frac{1}{3}\times \frac{1}{x}$$

Raise -105 to the power 1.

$$-105\times \frac{1}{3}\times \frac{1}{x}$$

Multiply -105 times \frac{1}{3}.

$$-35\times \frac{1}{x}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-105\right)^{1}x^{3}}{3^{1}x^{4}}$$

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

$$\frac{\left(-105\right)^{1}x^{3-4}}{3^{1}}$$

Subtract 4 from 3.

$$\frac{\left(-105\right)^{1}\times \frac{1}{x}}{3^{1}}$$

Divide -105 by 3.

$$-35\times \frac{1}{x}$$

Differentiate w.r.t. x

$$\frac{35}{x^{2}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{105}{3}\right)x^{3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(-35\times \frac{1}{x})$$

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$-\left(-35\right)x^{-1-1}$$

Do the arithmetic.

$$35x^{-2}$$