Solve 4x^2*40x^2*25^2

$$4 { x }^{ 2 } \times 40 { x }^{ 2 } \times { 25 }^{ 2 }$$

Evaluate

$$100000x^{4}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$4x^{4}\times 40\times 25^{2}$$

Multiply 4 and 40 to get 160.

$$160x^{4}\times 25^{2}$$

Calculate 25 to the power of 2 and get 625.

$$160x^{4}\times 625$$

Multiply 160 and 625 to get 100000.

$$100000x^{4}$$

Differentiate w.r.t. x

$$400000x^{3}$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}\times 40\times 25^{2})$$

Multiply 4 and 40 to get 160.

$$\frac{\mathrm{d}}{\mathrm{d}x}(160x^{4}\times 25^{2})$$

Calculate 25 to the power of 2 and get 625.

$$\frac{\mathrm{d}}{\mathrm{d}x}(160x^{4}\times 625)$$

Multiply 160 and 625 to get 100000.

$$\frac{\mathrm{d}}{\mathrm{d}x}(100000x^{4})$$

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

$$4\times 100000x^{4-1}$$

Multiply 4 times 100000.

$$400000x^{4-1}$$

Subtract 1 from 4.

$$400000x^{3}$$