Solve 8x^3y^5z^5/2x^2y3{z^5}

$$\frac{ 8 { x }^{ 3 } { y }^{ 5 } { z }^{ 5 } }{ 2 { x }^{ 2 } y3 { z }^{ 5 } }$$

Differentiate w.r.t. x

$$\frac{4y^{5}}{y_{3}}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{8y^{5}z^{5}}{2y_{3}z^{5}}x^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{4y^{5}}{y_{3}}x^{1})$$

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}.

$$\frac{4y^{5}}{y_{3}}x^{1-1}$$

Do the arithmetic.

$$\frac{4y^{5}}{y_{3}}x^{0}$$

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

$$\frac{4y^{5}}{y_{3}}\times 1$$

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

$$\frac{4y^{5}}{y_{3}}$$

Evaluate

$$\frac{4xy^{5}}{y_{3}}$$

Solution Steps

Cancel out 2x^{2}z^{5} in both numerator and denominator.

$$\frac{4xy^{5}}{y_{3}}$$