Solve -15ef^3g^2div(-40ef^2g)

$$- 15 e f ^ { 3 } g ^ { 2 } \div ( - 40 e f ^ { 2 } g )$$

Differentiate w.r.t. f

$$\frac{3g}{8}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}f}(\left(-\frac{15eg^{2}}{-40eg}\right)f^{3-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}f}(\frac{3g}{8}f^{1})$$

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}.

$$\frac{3g}{8}f^{1-1}$$

Do the arithmetic.

$$\frac{3g}{8}f^{0}$$

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

$$\frac{3g}{8}\times 1$$

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

$$\frac{3g}{8}$$

Evaluate

$$\frac{3fg}{8}$$

Solution Steps

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

$$\frac{-3fg}{-8}$$