Solve 410^6v^5-11v^5+8

$$410 ^ { 6 } v ^ { 5 } - 11 v ^ { 5 } + 8$$

Evaluate

$$4750104240999989v^{5}+8$$

Solution Steps

Calculate 410 to the power of 6 and get 4750104241000000.

$$4750104241000000v^{5}-11v^{5}+8$$

Combine 4750104241000000v^{5} and -11v^{5} to get 4750104240999989v^{5}.

$$4750104240999989v^{5}+8$$

Differentiate w.r.t. v

$$23750521204999945v^{4}$$

Steps Using Derivative Rule for Sum

Calculate 410 to the power of 6 and get 4750104241000000.

$$\frac{\mathrm{d}}{\mathrm{d}v}(4750104241000000v^{5}-11v^{5}+8)$$

Combine 4750104241000000v^{5} and -11v^{5} to get 4750104240999989v^{5}.

$$\frac{\mathrm{d}}{\mathrm{d}v}(4750104240999989v^{5}+8)$$

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}.

$$5\times 4750104240999989v^{5-1}$$

Multiply 5 times 4750104240999989.

$$23750521204999945v^{5-1}$$

Subtract 1 from 5.

$$23750521204999945v^{4}$$