Simple Derivatives
Find the derivative of:
f(x) = 10x(5x2)
What is f'(x) = 150x2?
Find the third derivative of: f(t) = 3t7 − 6t4 + 8t3 − 12t
What is f'''(t) = 630t4 - 144t + 48?
Find the tangent line of:
f(x) = cos(2x),
at x = 0
What is y = 1?
Differentiate using chain rule:
f(x) = cos(sin(tan(5x2)))
What is f'(x) = -10xsin(sin(tan(5x2)))cos(tan(5x2))sec2(5x2)?
Find the derivative of:
f(x) = -5x3 - 2x21
What is f'(x) = -15x2 - 42x20?
Find d2y/dx2 of:
2x3 + y2 = 1 − 4y
What is d2y/dx2 = [-6x(y+2)2 - 9x4] / [y+2]3
Find the tangent line of:
f(x) = 3x3 + 7x2 + x4,
at x = 3
What is y - 225 = 231(x - 3)?
Differentiate using chain rule:
y = x(4x+x5)1/3
What is y' = [8x5 + 16x] / [3(4x + x5)2/3]
Find the derivative of:
f(x) = 30x + (4x3 + 3) / 4
What is f'(x) = 30 + 3x2?
Find the second derivative of:
f(x) = cos2(7x)
What is f''(x) = -98cos(14x)?
Find the tangent line of:
f(x) = 7x / (x2 + 12),
at x = 4
What is y = -x/28 + 8/7?
Differentiate using chain rule:
f(t) = sin-4/3(2t / (t2 + 10))
What is f'(t) = [8cos(2t / (t2 + 10))(t2 - 10)] / [3sin7/3(2t / (t2 + 10))(t2 + 10)2]?
Find the derivative of:
f(x) = tan(x)sin(x)cos(x)
What is f'(x) = sin(2x)?
Find the second derivative of:
f(x) = sin(2x3 − 9x)
What is f''(x) = -sin(2x3 - 9x)(6x2 - 9)2 + 12xcos(2x3 - 9x)?
Find the tangent line of:
f(x) = 15x2(30x3 + 15x),
at x = 2
What is y - 16200 = 38700(x - 2)?
Differentiate using chain rule:
y = sec-4(4+x3) / 5
What is y' = (-12x2/5)cos4(4+x3)tan(4+x3)?
Find the derivative of:
f(x) = 30x / (sin(x)cos(x))
What is f'(x) = (15sin(2x) - 30xcos(2x)) / (cos(x)sin(x))2?
Find the third derivative of:
f(t) = sec(5t)
What is f'''(t) = 625sec3(5x)tan(5x) + 125tan3(5x)sec(5x)?
Find the tangent line of:
f(x) = 2x + sin(2x),
at x = 0
What is y = 4x?
Differentiate using chain rule:
y = 10(1+(2-(6+7x4)9)3)5
What is
y' = -37800x3(1+(2-(6+7x4)9)3)4(2-(6+7x4)9)2(6+7x4)8?