Solve d(3^5)^2=

$$d ( 3 ^ { 5 } ) ^ { 2 } =$$

Evaluate

$$59049d$$

Solution Steps

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$d\times 3^{10}$$

Calculate 3 to the power of 10 and get 59049.

$$d\times 59049$$

Differentiate w.r.t. d

$$59049$$

Steps Using Definition of a Derivative

To raise a power to another power, multiply the exponents. Multiply 5 and 2 to get 10.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d\times 3^{10})$$

Calculate 3 to the power of 10 and get 59049.

$$\frac{\mathrm{d}}{\mathrm{d}d}(d\times 59049)$$

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

$$59049d^{1-1}$$

Subtract 1 from 1.

$$59049d^{0}$$

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

$$59049\times 1$$

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

$$59049$$