Solve 4x^2*4x+1

$$4 x ^ { 2 } \cdot 4 x + 1$$

Evaluate

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

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

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

Multiply 4 and 4 to get 16.

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

Differentiate w.r.t. x

$$48x^{2}$$

Steps Using Derivative Rule for Sum

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x^{3}\times 4+1)$$

Multiply 4 and 4 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}x}(16x^{3}+1)$$

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}.

$$3\times 16x^{3-1}$$

Multiply 3 times 16.

$$48x^{3-1}$$

Subtract 1 from 3.

$$48x^{2}$$