Solve BB^5+110^5+84^5+27^5

$$B B ^ { 5 } + 110 ^ { 5 } + 84 ^ { 5 } + 27 ^ { 5 }$$

Evaluate

$$B^{6}[phone]$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$B^{6}+110^{5}+84^{5}+27^{5}$$

Calculate 110 to the power of 5 and get 16105100000.

$$B^{6}[phone]+84^{5}+27^{5}$$

Calculate 84 to the power of 5 and get 4182119424.

$$B^{6}[phone]+4182119424+27^{5}$$

Add 16105100000 and 4182119424 to get 20287219424.

$$B^{6}[phone]+27^{5}$$

Calculate 27 to the power of 5 and get 14348907.

$$B^{6}[phone]+14348907$$

Add 20287219424 and 14348907 to get 20301568331.

$$B^{6}[phone]$$

Differentiate w.r.t. B

$$6B^{5}$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 1 and 5 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}+110^{5}+84^{5}+27^{5})$$

Calculate 110 to the power of 5 and get 16105100000.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}[phone]+84^{5}+27^{5})$$

Calculate 84 to the power of 5 and get 4182119424.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}[phone]+4182119424+27^{5})$$

Add 16105100000 and 4182119424 to get 20287219424.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}[phone]+27^{5})$$

Calculate 27 to the power of 5 and get 14348907.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}[phone]+14348907)$$

Add 20287219424 and 14348907 to get 20301568331.

$$\frac{\mathrm{d}}{\mathrm{d}B}(B^{6}[phone])$$

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}.

$$6B^{6-1}$$

Subtract 1 from 6.

$$6B^{5}$$