Solve f(x)=3x^2-1quadg(x)sqrt{x}+5

$$f ( x ) = 3 x ^ { 2 } - 1 \quad g ( x ) \sqrt { x } + 5$$

Differentiate w.r.t. x

$$-\frac{3\sqrt{x}g}{2}+6x$$

Steps Using Derivative Rule for Sum

Multiply -1 and 1 to get -1.

$$\frac{\mathrm{d}}{\mathrm{d}x}(3x^{2}-gx\sqrt{x}+5)$$

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}.

$$2\times 3x^{2-1}+\left(-\sqrt{x}g\right)x^{1-1}$$

Multiply 2 times 3.

$$6x^{2-1}+\left(-\sqrt{x}g\right)x^{1-1}$$

Subtract 1 from 2.

$$6x^{1}+\left(-\sqrt{x}g\right)x^{1-1}$$

Subtract 1 from 1.

$$6x^{1}+\left(-\sqrt{x}g\right)x^{0}$$

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

$$6x+\left(-\sqrt{x}g\right)x^{0}$$

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

$$6x+\left(-\sqrt{x}g\right)\times 1$$

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

$$6x-\sqrt{x}g$$

Evaluate

$$3x^{2}-gx^{\frac{3}{2}}+5$$