Solve 4^2*5x^2

$${ 4 }^{ 2 } \times 5 { x }^{ 2 }$$

Evaluate

$$80x^{2}$$

Solution Steps

Calculate 4 to the power of 2 and get 16.

$$16\times 5x^{2}$$

Multiply 16 and 5 to get 80.

$$80x^{2}$$

Differentiate w.r.t. x

$$160x$$

Steps Using Definition of a Derivative

Calculate 4 to the power of 2 and get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16\times 5x^{2})$$

Multiply 16 and 5 to get 80.

$$\frac{\mathrm{d}}{\mathrm{d}x}(80x^{2})$$

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

$$2\times 80x^{2-1}$$

Multiply 2 times 80.

$$160x^{2-1}$$

Subtract 1 from 2.

$$160x^{1}$$

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

$$160x$$