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Solve the differential equation: dy/dx = tan^3(x)sec^2(x)

dy/dx = tan 3 (x)sec 2 (x) Integrate both sides ==> ∫dy= ∫ tan 3 (x)sec 2 (x) dx Use the substitution u=tan(x) And by differentiation du/dx = sec 2 (x) , which leads to dx = du/sec 2 (x) ==> and subbin...
RS
Answered by Ryan S. • Maths tutor
12975 Views

Differentiate x^(1/2)ln(3x) with respect to x.

First we notice that this is a product of two functions of x, so we are going to use the product rule. Recall (uv)'(x)=u'(x)v(x)+v'(x)u(x). Let u(x)=x^(1/2) and v(x)=ln(3x). We need to find u'(x) and v'(x). ...
AR
Answered by Aidan R. • Maths tutor
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Identify the stationary points of f(x)=3x^3+2x^2+4 (by finding the first and second derivative) and determine their nature.

f'(x)=9x 2 ​+4x, and f''(x)=18x+4 (derivatives) f'(x)=0 at x=0 or x=-4/9 when x=0 f''(x)>0 therefore a minimum value, when x=-4/9 f''(x)<0 and thus a maximum value.
SO
Answered by Sieff O. • Maths tutor
4331 Views

Find values of x for which 2x^2 < 5x + 12

Start by rearranging the inequality - make sure the sign next to the x 2 term is positive to make it easier: 2x 2 -5x - 12&lt; 0 Next step is to factorise this quadratic. To do this, remember that the genera...
SB
Answered by Sean B. • Maths tutor
16013 Views

Differentiate y=(x^2+1)(e^-x)

Here, we're using the product rule (and the chain rule for the e -x ): y=(x 2 +1)(e -x ) dy/dx=(2x)(e -x )+(x 2 +1)(-1)(e -x ) Then we simplify to get: dy/dx=(e -x )(2x-x 2 -1)
RD
Answered by Rishav D. • Maths tutor
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