Solve 77x^4/35x

$$\frac { 77 x ^ { 4 } } { 35 x }$$

Evaluate

$$\frac{11x^{3}}{5}$$

Steps for Quotient of Exponentials

Use the rules of exponents to simplify the expression.

$$\frac{77^{1}x^{4}}{35^{1}x^{1}}$$

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

$$\frac{77^{1}x^{4-1}}{35^{1}}$$

Subtract 1 from 4.

$$\frac{77^{1}x^{3}}{35^{1}}$$

Reduce the fraction \frac{77}{35} to lowest terms by extracting and canceling out 7.

$$\frac{11}{5}x^{3}$$

Differentiate w.r.t. x

$$\frac{33x^{2}}{5}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{77}{35}x^{4-1})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{11}{5}x^{3})$$

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}.

$$3\times \frac{11}{5}x^{3-1}$$

Do the arithmetic.

$$\frac{33}{5}x^{2}$$