Solve f(4*10^6)*(7*10^9)

$$f ( 4 \times 10 ^ { 6 } ) \times ( 7 \times 10 ^ { 9 } )$$

Evaluate

$$28000000000000000f$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$f\times 4\times 10^{15}\times 7$$

Calculate 10 to the power of 15 and get 1000000000000000.

$$f\times 4\times 1000000000000000\times 7$$

Multiply 4 and 1000000000000000 to get 4000000000000000.

$$f\times 4000000000000000\times 7$$

Multiply 4000000000000000 and 7 to get 28000000000000000.

$$f\times 28000000000000000$$

Differentiate w.r.t. f

$$28000000000000000$$

Steps Using Definition of a Derivative

To multiply powers of the same base, add their exponents. Add 6 and 9 to get 15.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 4\times 10^{15}\times 7)$$

Calculate 10 to the power of 15 and get 1000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 4\times 1000000000000000\times 7)$$

Multiply 4 and 1000000000000000 to get 4000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 4000000000000000\times 7)$$

Multiply 4000000000000000 and 7 to get 28000000000000000.

$$\frac{\mathrm{d}}{\mathrm{d}f}(f\times 28000000000000000)$$

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

$$28000000000000000f^{1-1}$$

Subtract 1 from 1.

$$28000000000000000f^{0}$$

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

$$28000000000000000\times 1$$

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

$$28000000000000000$$