Solve f(-3)^2*(-5)^2/(-5)^6

$$f \frac { ( - 3 ) ^ { 2 } \times ( - 5 ) ^ { 2 } } { ( - 5 ) ^ { 6 } }$$

Evaluate

$$\frac{9f}{625}$$

Solution Steps

Cancel out \left(-5\right)^{2} in both numerator and denominator.

$$f\times \frac{\left(-3\right)^{2}}{\left(-5\right)^{4}}$$

Calculate -3 to the power of 2 and get 9.

$$f\times \frac{9}{\left(-5\right)^{4}}$$

Calculate -5 to the power of 4 and get 625.

$$f\times \frac{9}{625}$$

Differentiate w.r.t. f

$$\frac{9}{625} = 0.0144$$

Steps Using Definition of a Derivative

Cancel out \left(-5\right)^{2} in both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{\left(-3\right)^{2}}{\left(-5\right)^{4}})$$

Calculate -3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{9}{\left(-5\right)^{4}})$$

Calculate -5 to the power of 4 and get 625.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times \frac{9}{625})$$

The derivative of ax^{n} is nax^{n-1}.

$$\frac{9}{625}f^{1-1}$$

Subtract 1 from 1.

$$\frac{9}{625}f^{0}$$

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

$$\frac{9}{625}\times 1$$

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

$$\frac{9}{625}$$