Solve x^2/4^-4

$$\frac { x ^ { 2 } } { 4 ^ { - 4 } }$$

Evaluate

$$256x^{2}$$

Solution Steps

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{x^{2}}{\frac{1}{256}}$$

Divide x^{2} by \frac{1}{256} by multiplying x^{2} by the reciprocal of \frac{1}{256}.

$$x^{2}\times 256$$

Differentiate w.r.t. x

$$512x$$

Steps Using Definition of a Derivative

Calculate 4 to the power of -4 and get \frac{1}{256}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{2}}{\frac{1}{256}})$$

Divide x^{2} by \frac{1}{256} by multiplying x^{2} by the reciprocal of \frac{1}{256}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x^{2}\times 256)$$

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

$$2\times 256x^{2-1}$$

Multiply 2 times 256.

$$512x^{2-1}$$

Subtract 1 from 2.

$$512x^{1}$$

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

$$512x$$