Solve 42x^2*3x^-4

$$42 x ^ { 2 } \times 3 x ^ { - 4 }$$

Evaluate

$$\frac{126}{x^{2}}$$

Solution Steps

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

$$42x^{-2}\times 3$$

Multiply 42 and 3 to get 126.

$$126x^{-2}$$

Differentiate w.r.t. x

$$-\frac{252}{x^{3}}$$

Steps Using Definition of a Derivative

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

$$\frac{\mathrm{d}}{\mathrm{d}x}(42x^{-2}\times 3)$$

Multiply 42 and 3 to get 126.

$$\frac{\mathrm{d}}{\mathrm{d}x}(126x^{-2})$$

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

$$-2\times 126x^{-2-1}$$

Multiply -2 times 126.

$$-252x^{-2-1}$$

Subtract 1 from -2.

$$-252x^{-3}$$