Solve 5x^2*3^2

$$5 x ^ { 2 } \times 3 ^ { 2 }$$

Evaluate

$$45x^{2}$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$5x^{2}\times 9$$

Multiply 5 and 9 to get 45.

$$45x^{2}$$

Differentiate w.r.t. x

$$90x$$

Steps Using Definition of a Derivative

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(5x^{2}\times 9)$$

Multiply 5 and 9 to get 45.

$$\frac{\mathrm{d}}{\mathrm{d}x}(45x^{2})$$

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

$$2\times 45x^{2-1}$$

Multiply 2 times 45.

$$90x^{2-1}$$

Subtract 1 from 2.

$$90x^{1}$$

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

$$90x$$