Solve 5^4+45^3+95^2+105+k

$$5 ^ { 4 } + 45 ^ { 3 } + 95 ^ { 2 } + 105 + k$$

Evaluate

$$k+100880$$

Solution Steps

Calculate 5 to the power of 4 and get 625.

$$625+45^{3}+95^{2}+105+k$$

Calculate 45 to the power of 3 and get 91125.

$$625+91125+95^{2}+105+k$$

Add 625 and 91125 to get 91750.

$$91750+95^{2}+105+k$$

Calculate 95 to the power of 2 and get 9025.

$$91750+9025+105+k$$

Add 91750 and 9025 to get 100775.

$$100775+105+k$$

Add 100775 and 105 to get 100880.

$$100880+k$$

Differentiate w.r.t. k

$$1$$

Steps Using Derivative Rule for Sum

Calculate 5 to the power of 4 and get 625.

$$\frac{\mathrm{d}}{\mathrm{d}k}(625+45^{3}+95^{2}+105+k)$$

Calculate 45 to the power of 3 and get 91125.

$$\frac{\mathrm{d}}{\mathrm{d}k}(625+91125+95^{2}+105+k)$$

Add 625 and 91125 to get 91750.

$$\frac{\mathrm{d}}{\mathrm{d}k}(91750+95^{2}+105+k)$$

Calculate 95 to the power of 2 and get 9025.

$$\frac{\mathrm{d}}{\mathrm{d}k}(91750+9025+105+k)$$

Add 91750 and 9025 to get 100775.

$$\frac{\mathrm{d}}{\mathrm{d}k}(100775+105+k)$$

Add 100775 and 105 to get 100880.

$$\frac{\mathrm{d}}{\mathrm{d}k}(100880+k)$$

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}.

$$k^{1-1}$$

Subtract 1 from 1.

$$k^{0}$$

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

$$1$$