Solve 4left(x^2right)^2+4x-1

$$4 { \left( { x }^{ 2 } \right) }^{ 2 } +4x-1$$

Differentiate w.r.t. x

$$16x^{3}+4$$

Steps Using Derivative Rule for Sum

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{4}+4x-1)$$

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}.

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

Multiply 4 times 4.

$$16x^{4-1}+4x^{1-1}$$

Subtract 1 from 4.

$$16x^{3}+4x^{1-1}$$

Subtract 1 from 1.

$$16x^{3}+4x^{0}$$

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

$$16x^{3}+4\times 1$$

For any term t, t\times 1=t and 1t=t.

$$16x^{3}+4$$

Evaluate

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

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 2 and 2 to get 4.

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