Solve 4^2*d^2*(4*d^4)=

$$4 ^ { 2 } \cdot d ^ { 2 } \cdot ( 4 \cdot d ^ { 4 } ) =$$

Evaluate

$$64d^{6}$$

Solution Steps

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

$$4^{3}d^{2}d^{4}$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$4^{3}d^{6}$$

Calculate 4 to the power of 3 and get 64.

$$64d^{6}$$

Differentiate w.r.t. d

$$384d^{5}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}d}(4^{3}d^{2}d^{4})$$

To multiply powers of the same base, add their exponents. Add 2 and 4 to get 6.

$$\frac{\mathrm{d}}{\mathrm{d}d}(4^{3}d^{6})$$

Calculate 4 to the power of 3 and get 64.

$$\frac{\mathrm{d}}{\mathrm{d}d}(64d^{6})$$

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

$$6\times 64d^{6-1}$$

Multiply 6 times 64.

$$384d^{6-1}$$

Subtract 1 from 6.

$$384d^{5}$$