Solve 3x^-3x^4^5/9x^4=

$$\frac { 3 x ^ { - 3 } x ^ { 4 ^ { 5 } } } { 9 x ^ { 4 } } =$$

Evaluate

$$\frac{x^{1017}}{3}$$

Solution Steps

Cancel out 3 in both numerator and denominator.

$$\frac{x^{-3}x^{4^{5}}}{3x^{4}}$$

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

$$\frac{x^{4^{5}}}{3x^{7}}$$

Calculate 4 to the power of 5 and get 1024.

$$\frac{x^{1024}}{3x^{7}}$$

Cancel out x^{7} in both numerator and denominator.

$$\frac{x^{1017}}{3}$$

Differentiate w.r.t. x

$$339x^{1016}$$

Solution Steps

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{3x^{1024}}{9}x^{-3-4})$$

Do the arithmetic.

$$\frac{\mathrm{d}}{\mathrm{d}x}(\frac{x^{1024}}{3}x^{-7})$$

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}.

$$-7\times \frac{x^{1024}}{3}x^{-7-1}$$

Do the arithmetic.

$$\left(-\frac{7x^{1024}}{3}\right)x^{-8}$$