Question

**FIND THE DERIVATIVE / DIFFERENTIATE VARIOUS FUNCTIONS f'(x) using chain rule/power rule and**

** differentiation:**

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1) f(x) = 10sin (2x^{2} + 3) - 11csc (2x^{2} + 3) + 8

2) f(x) = ln ((8x^{3} + 2e^{6x^4 + 1})^{6} (4x^{2} + 9)^{10})

3) f(x) = 2x^{3} + 3x + 1 / x^{2} + 5

4) f(x) = 9e^{sec(x)} + 8ln(cos(x))

5) f(x) = 8sin (3x^{2} + 6x + 1) + 2tan (3x^{2} + 6x + 1)

6) f(x) = 7x^{2} + 1 / 5x - 9

**These are the solutions:**

1) f'(x) = 40(x) cos (2x^{2} + 3) + 44(x) csc (2x^{2} + 3) * cot (2x^{2} + 3)

2) f'(x) = (72x^{2} + 144x^{3}e^{6x^4+1} / 4x^{3} + e^{6x^4+1}) + 10 (8x / 4x^{2} + 9)

3) f'(x) = 2x^{4} + 27x^{2} - 2x +15 / (x^{2} + 5)^{2}

4) f'(x) = 9sec(x) tan(x) e^{sec(x)} - 8tan(x)

5) f'(x) = (48x + 48) cos(3x^{2} + 6x + 1) + (12x + 12) sec^{2}(3x^{2} +6x + 1)

6) f'(x) = (35x^{2} - 126x -5) / (5x - 9)^{2}

Please provide all steps, thank you!

#### Top Answer

1) f'(x) = 40(x) cos (2x 2 + 3) + 44(x) csc (2x 2 + 3) * cot (2x 2 + 3) 2) f'(x) = (72x 2 + 144x 3... View the full answer