Solve 45x74^2x457^2

$$45x { 74 }^{ 2 } x { 457 }^{ 2 }$$

Evaluate

$$51464570580x^{2}$$

Solution Steps

Multiply x and x to get x^{2}.

$$45x^{2}\times 74^{2}\times 457^{2}$$

Calculate 74 to the power of 2 and get 5476.

$$45x^{2}\times 5476\times 457^{2}$$

Multiply 45 and 5476 to get 246420.

$$246420x^{2}\times 457^{2}$$

Calculate 457 to the power of 2 and get 208849.

$$246420x^{2}\times 208849$$

Multiply 246420 and 208849 to get 51464570580.

$$51464570580x^{2}$$

Differentiate w.r.t. x

$$102929141160x$$

Steps Using Definition of a Derivative

Multiply x and x to get x^{2}.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{2}\times 74^{2}\times 457^{2})$$

Calculate 74 to the power of 2 and get 5476.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{2}\times 5476\times 457^{2})$$

Multiply 45 and 5476 to get 246420.

$$\frac{\mathrm{d}}{\mathrm{d}x}(246420x^{2}\times 457^{2})$$

Calculate 457 to the power of 2 and get 208849.

$$\frac{\mathrm{d}}{\mathrm{d}x}(246420x^{2}\times 208849)$$

Multiply 246420 and 208849 to get 51464570580.

$$\frac{\mathrm{d}}{\mathrm{d}x}(51464570580x^{2})$$

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

$$2\times 51464570580x^{2-1}$$

Multiply 2 times 51464570580.

$$102929141160x^{2-1}$$

Subtract 1 from 2.

$$102929141160x^{1}$$

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

$$102929141160x$$