Solve d^10*d^20

$$d ^ { 10 } \times d ^ { 20 }$$

Differentiate w.r.t. d

$$30d^{29}$$

Steps Using Derivative Rule for Product

For any two differentiable functions, the derivative of the product of two functions is the first function times the derivative of the second plus the second function times the derivative of the first.

$$d^{10}\frac{\mathrm{d}}{\mathrm{d}d}(d^{20})+d^{20}\frac{\mathrm{d}}{\mathrm{d}d}(d^{10})$$

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}.

$$d^{10}\times 20d^{20-1}+d^{20}\times 10d^{10-1}$$

Simplify.

$$d^{10}\times 20d^{19}+d^{20}\times 10d^{9}$$

To multiply powers of the same base, add their exponents.

$$20d^{10+19}+10d^{20+9}$$

Simplify.

$$20d^{29}+10d^{29}$$

Evaluate

$$d^{30}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 10 and 20 to get 30.

$$d^{30}$$