Solve 1+8f(2f*1)

$$1 + 8 f ( 2 f \cdot 1 )$$

Evaluate

$$16f^{2}+1$$

Solution Steps

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

$$1+8f^{2}\times 2\times 1$$

Multiply 8 and 2 to get 16.

$$1+16f^{2}\times 1$$

Multiply 16 and 1 to get 16.

$$1+16f^{2}$$

Differentiate w.r.t. f

$$32f$$

Steps Using Derivative Rule for Sum

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

$$\frac{\mathrm{d}}{\mathrm{d}f}(1+8f^{2}\times 2\times 1)$$

Multiply 8 and 2 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}f}(1+16f^{2}\times 1)$$

Multiply 16 and 1 to get 16.

$$\frac{\mathrm{d}}{\mathrm{d}f}(1+16f^{2})$$

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}.

$$2\times 16f^{2-1}$$

Multiply 2 times 16.

$$32f^{2-1}$$

Subtract 1 from 2.

$$32f^{1}$$

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

$$32f$$