Solve (-35x^2)div(-7x)=

$$(-35 { x }^{ 2 } ) \div (-7x)=$$

Evaluate

$$5x$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{\left(-35\right)^{1}x^{2}}{\left(-7\right)^{1}x^{1}}$$

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

$$\frac{\left(-35\right)^{1}x^{2-1}}{\left(-7\right)^{1}}$$

Subtract 1 from 2.

$$\frac{\left(-35\right)^{1}x^{1}}{\left(-7\right)^{1}}$$

Divide -35 by -7.

$$5x^{1}$$

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

$$5x$$

Differentiate w.r.t. x

$$5$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\left(-\frac{35}{-7}\right)x^{2-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{1})$$

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}.

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

Do the arithmetic.

$$5x^{0}$$

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

$$5\times 1$$

For any term t, t\times 1=t and 1t=t.

$$5$$