Solve 4x+3^26x-2-5x+4

$$4 x + 3 ^ { 2 } 6 x - 2 - 5 x + 4$$

Evaluate

$$53x+2$$

Solution Steps

Calculate 3 to the power of 2 and get 9.

$$4x+9\times 6x-2-5x+4$$

Multiply 9 and 6 to get 54.

$$4x+54x-2-5x+4$$

Combine 4x and 54x to get 58x.

$$58x-2-5x+4$$

Combine 58x and -5x to get 53x.

$$53x-2+4$$

Add -2 and 4 to get 2.

$$53x+2$$

Differentiate w.r.t. x

$$53$$

Steps Using Derivative Rule for Sum

Calculate 3 to the power of 2 and get 9.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+9\times 6x-2-5x+4)$$

Multiply 9 and 6 to get 54.

$$\frac{\mathrm{d}}{\mathrm{d}x}(4x+54x-2-5x+4)$$

Combine 4x and 54x to get 58x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(58x-2-5x+4)$$

Combine 58x and -5x to get 53x.

$$\frac{\mathrm{d}}{\mathrm{d}x}(53x-2+4)$$

Add -2 and 4 to get 2.

$$\frac{\mathrm{d}}{\mathrm{d}x}(53x+2)$$

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}.

$$53x^{1-1}$$

Subtract 1 from 1.

$$53x^{0}$$

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

$$53\times 1$$

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

$$53$$