Solve xsqrt{{left(7/47right)}^8+8}

$$x \sqrt{ { \left( \frac{ 7 }{ 47 } \right) }^{ 8+8 } }$$

Evaluate

$$\frac{5764801x}{23811286661761}$$

Solution Steps

Add 8 and 8 to get 16.

$$x\sqrt{\left(\frac{7}{47}\right)^{16}}$$

Calculate \frac{7}{47} to the power of 16 and get \frac{33232930569601}{566977372488557307219621121}.

$$x\sqrt{\frac{33232930569601}{566977372488557307219621121}}$$

Rewrite the square root of the division \frac{33232930569601}{566977372488557307219621121} as the division of square roots \frac{\sqrt{33232930569601}}{\sqrt{566977372488557307219621121}}. Take the square root of both numerator and denominator.

$$x\times \frac{5764801}{23811286661761}$$

Differentiate w.r.t. x

$$\frac{5764801}{23811286661761} = 2.421037166906988 \times 10^{-7}$$

Steps Using Definition of a Derivative

Add 8 and 8 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\left(\frac{7}{47}\right)^{16}})$$

Calculate \frac{7}{47} to the power of 16 and get \frac{33232930569601}{566977372488557307219621121}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\sqrt{\frac{33232930569601}{566977372488557307219621121}})$$

Rewrite the square root of the division \frac{33232930569601}{566977372488557307219621121} as the division of square roots \frac{\sqrt{33232930569601}}{\sqrt{566977372488557307219621121}}. Take the square root of both numerator and denominator.

$$\frac{\mathrm{d}}{\mathrm{d}x}(x\times \frac{5764801}{23811286661761})$$

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

$$\frac{5764801}{23811286661761}x^{1-1}$$

Subtract 1 from 1.

$$\frac{5764801}{23811286661761}x^{0}$$

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

$$\frac{5764801}{23811286661761}\times 1$$

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

$$\frac{5764801}{23811286661761}$$