Solve frac{c^{4}d^{4}f^3}{c^2d^4f^3}

$$\frac { c ^ { 4 } d ^ { 4 } f ^ { 3 } } { c ^ { 2 } d ^ { 4 } f ^ { 3 } }$$

Differentiate w.r.t. c

$$2c$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}c}(\frac{f^{3}d^{4}}{f^{3}d^{4}}c^{4-2})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}c}(c^{2})$$

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}.

$$2c^{2-1}$$

Do the arithmetic.

$$2c^{1}$$

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

$$2c$$

Evaluate

$$c^{2}$$

Solution Steps

Cancel out c^{2}f^{3}d^{4} in both numerator and denominator.

$$c^{2}$$